Breusch–Pagan test

Breusch–Pagan test is a statistical test named after Trevor Breusch and Adrian Pagan. The test is used to detect heteroscedasticity in a linear regression model. Heteroscedasticity occurs when the variance of the errors from a regression model is not constant. This can lead to inefficiencies in the estimates of the model's parameters and to incorrect conclusions from hypothesis tests. The Breusch–Pagan test is one of the tools available for identifying the presence of heteroscedasticity.

Overview

The test involves regressing the squared residuals from the original regression model on the independent variables of that model. The null hypothesis of the test is that the errors are homoscedastic, meaning their variance is constant across observations. A significant test result indicates the presence of heteroscedasticity, suggesting that an alternative modeling approach may be necessary.

Procedure

To perform the Breusch–Pagan test, one follows these steps:

1. Estimate the original regression model and compute the residuals.
2. Square the residuals.
3. Regress the squared residuals on the original independent variables.
4. Compute the test statistic, which is based on the R-squared value from the regression in step 3 and the number of observations. The test statistic follows a chi-squared distribution with degrees of freedom equal to the number of independent variables in the model.
5. Compare the test statistic to the critical value from the chi-squared distribution to determine whether to reject the null hypothesis of homoscedasticity.

Applications

The Breusch–Pagan test is widely used in econometrics and other fields where regression analysis is common. It is particularly important in studies where the validity of inference relies on the assumption of homoscedasticity. Examples include finance, where the test can be used to validate models of asset returns, and health sciences, for models relating to patient outcomes.

Limitations

While the Breusch–Pagan test is a useful tool for detecting heteroscedasticity, it has limitations. It may not be powerful in detecting certain types of heteroscedasticity, and its performance can be affected by the choice of independent variables in the model. Additionally, the test assumes that the model is correctly specified, meaning that all relevant variables are included and the functional form is correct.

See Also

• Linear regression
• Heteroscedasticity
• White test, another test for heteroscedasticity
• Goldfeld–Quandt test, an alternative test for heteroscedasticity