The Role of the Breusch-Pagan Test in EconometricsByRoberto PedacefromEconometrics For DummiesThe Breusch-Pagan (BP) test is one of the most common tests for heteroskedasticity. It begins by allowing the heteroskedasticity process to be a function of one or more of your independent variables, and its usually applied by assuming that heteroskedasticity may be a linear function of all the independent variables in the model. This assumption can be expressed as

The values for

arent known in practice, so the

are calculated from the residuals and used as proxies for

Generally, the BP test is based on the estimation of

Alternatively, a BP test can be performed by estimatingHeres how to perform a BP test:1. Estimate your model using OLS:

2. Obtain the predictedYvalues after estimating the model.3. Estimate the auxiliary regression using OLS:

4. From this auxiliary regression, retain the R-squared value:

5. Calculate theF-statistic or the chi-squared statistic:

The degrees of freedom for theF-test are equal to 1 in the numerator andn 2 in the denominator. The degrees of freedom for the chi-squared test are equal to 1. If either of these test statistics is significant, then you have evidence of heteroskedasticity. If not, you fail to reject the null hypothesis of homoskedasticity.To see how the BP test works, use some data about Major League Baseball players. First, estimate a model with the natural log of the players contract value as the dependent variable and several player characteristics as independent variables, including three-year averages for the players slugging percentage and at-bats, the players age, and the players tenure with the current team.Then run the BP test in STATA, which retains the predictedYvalues, estimates the auxiliary regression internally, and reports the chi-squared test. You can also request that STATA conduct theF-test version of the test.Both results are shown in the figure, and theyre consistent in rejecting the null hypothesis of homoskedasticity. Therefore, the statistical evidence implies that heteroskedasticity is present.

A weakness of the BP test is that it assumes the heteroskedasticity is a linear function of the independent variables. Failing to find evidence of heteroskedasticity with the BP doesnt rule out a nonlinear relationship between the independent variable(s) and the error variance. Additionally, the BP test isnt useful for determining how to correct or adjust the model for heteroskedasticity