Versions of White Test

[Ellin Handrason]

Dear Everyone,

I've done standard White Test for heteroscedasticity. First I made a linear regression, found R^2 = 0,3491 and then multiplied it by the number of observations (87). As a result, I got n*R^2 = 30,37. Chi-squared critical value with 7 degrees of freedom is 14,067 at 5% significance level. Hence, the obtained value of the test statistic exceeds the critical value, which means that the null hypothesis of homoscedasticity is rejected.

Then I did another version of White test using the following command: estat imtest, white. And I got chi2(19) = 23.00, Prob > chi2 = 0.2373. So, the null hypothesis of homoscedasticity is not rejected.

There is an apparent discrepancy between the result of the two versions of White Test. How can it be explained? Which version is more trustworthy?

[Carlo Lazzaro]

Ellin:
welcome to this forum.
Your research on this topic can surely benefit from Richard Williams 's outstanding teaching notes downloadable from https://www3.nd.edu/~rwilliam/stats2/l25.pdf.
Please follow the FAQ in your future posts and share what you typed and what Stata gave you back. Thanks.

[Richard Williams]

It sounds like you calculated the first test by hand. You don't seem to be using formulas I have in my notes, but they may be ok. You may have done it right, but let Stata do the calculations when it can. Stata is less likely to make a math mistake than you are. You probably want the command

estat hettest

Assuming the numbers are right, there is no necessary conflict between the two tests. imtest tosses in a lot of terms to account for nonlinear forms of hetero. If those terms are all trivial, they can potentially dilute the effects of the variables that do have significant effects.

More generally, it is often tempting to add a bunch of variables to a model "just in case" they have effects. But, adding a bunch of extraneous variables to a model can adversely affect your standard errors and significance tests. See

https://www3.nd.edu/~rwilliam/stats2/l41.pdf

Assuming your numbers are correct, I would assume homoskedasticity is violated, and would therefore try one of the remedies suggested in my handout that Carlos linked to.