Breusch-Pagan Test:

The Gold feld-Quandt test is sensitive to the number of central observations  omitted from  the data set. Secondly,  it is important  to  identify the variable X with which  the σ variance is related, as  the observations are arranged in increasing order of X.  

These limitations  of G-Q test is overcome by the B-P test.

The B-P test assumes the error term to be normally distributed. The steps given below are followed while carrying out the test.

• Estimate the regression model by OLS and obtain  the estimated residuals  ,
• Obtain,  which is the maximum likelihood estimator of variance  
• Construct  variable  p, defined as
• Regressp,  on Z, where Z  is a non-stochastic variable (any explanatory variable or combination of some explanatory variables can serve as Z)  such that
• Obtain ESS from the above  regressioil and takeas  the test statistic.

In the above θ follows chi-square distribution with (m-1)  degrees of freedom. We compare the θ value obtained above with  the critical value of chi-square.  If the observed value  of x² exceeds  the  critical value then the hypothesis  of hombscedasticity  is  rejected.

Most of the econometric software give results of the B-P test statistic.