A shortcut to Whites test. As noted in the text, the White test can consume degrees of

Question:

A shortcut to White’s test. As noted in the text, the White test can consume degrees of freedom if there are several regressors and if we introduce all the regressors, their squared terms, and their cross products. Therefore, instead of estimating regressions like Eq. (11.5.22), why not simply run the following regression:

û²_i = α₁ + α₂ Ŷ_i + α₂ Ŷ_2i + ν_i

where Ŷ_i are the estimated Y (i.e., regressand) values from whatever model you are estimating? After all, Ŷ_i is simply the weighted average of the regressors, with the estimated regression coefficients serving as the weights. Obtain the R² value from the preceding regression and use Eq. (11.5.22) to test the hypothesis that there is no heteroscedasticity. Apply the preceding test to the food expenditure example of Exercise 11.16.