# st: Re: white het. test

 From Christopher F Baum To statalist@hsphsun2.harvard.edu Subject st: Re: white het. test Date Sat, 14 Feb 2004 09:26:49 -0500

```On Feb 14, 2004, at 2:33 AM, Olena wrote:

```
I have to do a general (full) White heteroscedasticity test for my regression
with 9 variables. Number of unique variables (excluding constant) that should
be included in the regression of squared residuals on the cross-products of
x's is 39. When I manually run this auxiliary regression, Stata drops 2
variables. Resulting test statistic has Chi_2(37) distribtion. I get the same
result using whitetst command which I downloaded from the web. This command
relies on Stata's regress to keep only unique variables in the auxiliary
regression.
But when I use imtest, white , my test statistic is reported to have Chi_2(39)
distribution and it's value is slightly different from the one I obtain
manually.
So, my questions are: how does the imtest, white calculate the test statistic?
And how can I make Stata not to drop variables it finds collinear?
Thank you very much!

I cannot reproduce this behavior. whitetst drops the collinear squares and cross-products. In this example from -auto-, I have modified whitetst to report on its _rmcoll; it drops 6 regressors, leaving 14. ivhettest, as Mark Schaffer noted, will also produce this test. But imtest,white generates the same test statistic with 14 d.f. I do not see that imtest is failing to properly prune the regressor list.

Also note the 'whitetst, fitted' option; if you have a very large number of regressors, the d.f. of the standard White test will be prohibitively large. The alternate form, described in Wooldridge's text, uses products of the fitted values as regressors.

. regress

Source | SS df MS Number of obs = 74
-------------+------------------------------ F( 5, 68) = 8.87
Model | 250707635 5 50141527.1 Prob > F = 0.0000
Residual | 384357761 68 5652320.01 R-squared = 0.3948
Total | 635065396 73 8699525.97 Root MSE = 2377.5

------------------------------------------------------------------------ ------
price | Coef. Std. Err. t P>|t| [95% Conf. Interval]
------------- +----------------------------------------------------------------
mpg | -1002.389 461.152 -2.17 0.033 -1922.604 -82.1747
mpg2 | 20.10801 6.289746 3.20 0.002 7.557016 32.659
headroom | 5478.775 3711.48 1.48 0.145 -1927.368 12884.92
head2 | -712.0372 400.143 -1.78 0.080 -1510.51 86.4358
mh | -84.79946 94.36965 -0.90 0.372 -273.1112 103.5122
_cons | 13448.27 9733.056 1.38 0.172 -5973.738 32870.28
------------------------------------------------------------------------ ------

. whitetst
note: __00000D dropped due to collinearity
note: __00000E dropped due to collinearity
note: __00000H dropped due to collinearity
note: __00000K dropped due to collinearity
note: __00000N dropped due to collinearity
note: __00000S dropped due to collinearity

White's general test statistic : 9.428595 Chi-sq(14) P-value = .8027

. whitetst,fitted

White's special test statistic : 3.106367 Chi-sq( 2) P-value = .2116

. ivhettest
OLS heteroskedasticity test(s) using levels and cross products of all IVs
Ho: Disturbance is homoskedastic
White/Koenker nR2 test statistic : 9.429 Chi-sq(14) P-value = 0.8027

. imtest,white

White's test for Ho: homoskedasticity
against Ha: unrestricted heteroskedasticity

chi2(14) = 9.43
Prob > chi2 = 0.8027

Kit

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