How to use hettest for heteroskedasticity testing

[Dominic Berg]

Hi all,

I have a regression and want to test it for heteroskedasticity. Besides the dependent variable, the regression contains one explanatory variable that I want to check for significance and several control variables (that I'm not interested in in itself). My question is whether I have to include all controls in the hettest or whether it is sufficient when I only include the variable that I want to check for significance. Help would be great!

[Carlo Lazzaro]

Dominic:
there's no hard and fast rule about your query.
I usually go -estat hettest-, just to have a comprehensive picture.
Plotting residuals (see -help rvfplot- and -help -rvpplot-) can also be helpful (and sometimes much more helpful) than analytic tests.
That said, you can also test heteroskedasticity on an unique predictor via -estat szroeter-.
Eventually, you can also perform a decomposition test (see -help imtest-):

. sysuse auto.dta

. regress price mpg i.foreign

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     14.07
       Model |   180261702         2  90130850.8   Prob > F        =    0.0000
    Residual |   454803695        71  6405685.84   R-squared       =    0.2838
-------------+----------------------------------   Adj R-squared   =    0.2637
       Total |   635065396        73  8699525.97   Root MSE        =    2530.9

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -294.1955   55.69172    -5.28   0.000    -405.2417   -183.1494
             |
     foreign |
    Foreign  |   1767.292    700.158     2.52   0.014     371.2169    3163.368
       _cons |   11905.42   1158.634    10.28   0.000     9595.164    14215.67
------------------------------------------------------------------------------

. estat hettest

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity
         Ho: Constant variance
         Variables: fitted values of price

         chi2(1)      =     3.81
         Prob > chi2  =   0.0510

. estat szroeter mpg

Szroeter's test for homoskedasticity

    Ho: variance constant
    Ha: variance monotonic in mpg

         chi2(1)      =     8.05
         Prob > chi2  =   0.0046

. estat szroeter foreign

Szroeter's test for homoskedasticity

    Ho: variance constant
    Ha: variance monotonic in foreign

         chi2(1)      =     1.86
         Prob > chi2  =   0.1725

. estat imtest

Cameron & Trivedi's decomposition of IM-test

---------------------------------------------------
              Source |       chi2     df      p
---------------------+-----------------------------
  Heteroskedasticity |       5.26      4    0.2618
            Skewness |       5.26      2    0.0722
            Kurtosis |       1.27      1    0.2590
---------------------+-----------------------------
               Total |      11.79      7    0.1077
---------------------------------------------------

As an aside, please note that in some instances heteroskedasticity warns us about model misspecification (whisc is much more severe).