Breusch-Pagan Test
A statistical test used to detect the presence of heteroskedasticity in a linear regression model.
What is Breusch-Pagan Test?
The Breusch-Pagan test checks whether the variance of the errors in a regression is dependent on the values of the independent variables. It works by regressing the squared residuals from the original model on the original predictors. A significant test statistic indicates that the error variance is not constant (heteroskedasticity).
Why Breusch-Pagan Test Matters
Ordinary Least Squares (OLS) assumes homoskedasticity (constant variance of errors). If heteroskedasticity is present, OLS estimates remain unbiased, but the standard errors will be incorrect. This leads to invalid t-statistics and p-values, causing researchers to make false conclusions about statistical significance.
Example
A researcher regressing household expenditure on income performs a Breusch-Pagan test and finds significant heteroskedasticity, because the variation in spending is much wider for high-income households than for low-income ones. They must then use robust standard errors for valid inference.
Common Mistakes
- Assuming that the test detects all forms of heteroskedasticity; it specifically tests for linear forms of heteroskedasticity and may miss non-linear variance patterns.
- Using the test on small sample sizes where it lacks power, or assuming it is robust to extreme departures from normality.