There are a set of heteroscedasticity tests and remedies that require an assumption about the structure of the heteroscedasticity, if it exists. That is, to use these tests you must choose a specific functional form for the relationship between the error vriance and the variables that you believe determine the error variance. The major difference between these tests is the functional form that each test assumes.
The Breusch-Pagan test assumes the error variance is a linear function of one or more variables.
The Harvey-Godfrey test assumes the error variance is an exponential function of one or more variables. The variables are usually assumed to be one or more of the explanatory variables in the regression equation.
The white test of heteroscedasticity is a general test for the detection of heteroscdsticity existence in data set. It has the following advantages:
- It does not require you to specify a model of the structure of the heteroscedasticity, if it exists.
- It does not depend on the assumption that the errors are normally distributed.
- It specifically tests if the presence of heteroscedasticity causes the OLS formula for the variances and the covariances of the estimates to be incorrect.
Suppose that you find the evidence of existence of heteroscedasticity. If you use the oLS estimator, you will get unbiased but inefficient estimates of the parameters of the model. Also, the estimates of the variances and covariances of the parameter estimates will be biased and inconsistent, and as a result hypothesis tests will not be valid. When there is evidence of heteroscedasticity, econometricians do one of the two things:
- Use OLS estimator to estimate the parameters of the model. Correct the estimates of the variances and covariances of the OLS estimates so that they are consistent.
- Use an estimator other than the OLS estimator to estimate the parameters of the model.
Many econometricians choose first alternative. This is because the most serious consequence of using the OLS estimator when there is heteroscedasticity is that the estimates of the variances and covariances of the parameter estimates are biased and inconsistent. If this problem is corrected, then the only shortcoming of using OLS is that you lose some precision relative to some other estimator that you could have used. However, to get more precise estimates with an alternative estimator, you must know the approximate structure of the heteroscedasticity. If you specify the wrong model of heteroscedasticity, then this alternative estimator can yield estimates that are worse than the OLS