This is a modified version of the Breusch-Pagan test, which is less sensitive to the assumption of normality than the original test (Greene 1993, p. The test statistic for the Breusch-Pagan test is Where is the error variance for the ith observation and and are regression coefficients. The null hypothesis of the Breusch-Pagan test is The alternate hypothesis is that the error variance varies with a set of regressors, which are listed in the BREUSCH= option.ĭefine the matrix to be composed of the values of the variables listed in the BREUSCH= option, such that is the value of the jth variable in the BREUSCH= option for the ith observation. The null hypothesis for the modified Breusch-Pagan test is homosedasticity.
The WHITE option, on the other hand, produces the statistic discussed in Greene (1993). The SPEC option produces the test from Theorem 2 on page 823 of White (1980). Note that White’s test in the MODEL procedure is different than White’s test in the REG procedure requested by the SPEC option. Hence, P=5 with degrees of freedom, P–1=4. income*income occurs twice and one is dropped. In the example given below, the regressors are constant, income, income*income, income*income*income, and income*income*income*income. The statistic is asymptotically distributed as chi-squared with P–1 degrees of freedom, where P is the number of regressors in the regression, including the constant and n is the total number of observations. Where is the correlation coefficient obtained from the above regression. White’s test statistic is computed as follows: White’s test is equivalent to obtaining the error sum of squares for the regression of squared residuals on a constant and all the unique variables in, where the matrix J is composed of the partial derivatives of the equation residual with respect to the estimated parameters. Thus, White’s test might be significant when the errors are homoscedastic but the model is misspecified in other ways. Because of its generality, White’s test might identify specification errors other than heteroscedasticity (Thursby 1982). White’s test is general because it makes no assumptions about the form of the heteroscedasticity (White 1980). The WHITE option tests the null hypothesis The residuals of an estimation are used to investigate the heteroscedasticity of the true disturbances. For systems of equations, these tests are computed separately for the residuals of each equation. The MODEL procedure provides two tests for heteroscedasticity of the errors: White’s test and the modified Breusch-Pagan test.īoth White’s test and the Breusch-Pagan are based on the residuals of the fitted model.
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