Breusch-Pagan Test

[Lucca Mancini]

Hello

I am trying to do a Breusch-Pagan test to test for heteroscedasticity. I have two regression models with different dependent variables but with the same independent variables as follows

regress viol_crime_rate asylum_pop a8_pop lnpop benefit_claimants young_share
regress prop_crime_rate asylum_pop a8_pop lnpop benefit_claimants young_share

Should I do it as follows

regress viol_crime_rate asylum_pop a8_pop lnpop benefit_claimants young_share
estat hettest, fstat

regress prop_crime_rate asylum_pop a8_pop lnpop benefit_claimants young_share
estat hettest, fstat

Is this right?

or should I make just one test, since both models have the same independent but just different dependent variable as follows

​​​​​​​estat hettest asylum_pop a8_pop lnpop benefit_claimants young_share

I am confused, which way I should prefer and If the dependent variables play an important role.



Thank you very much for your help.

[Carlo Lazzaro]

Lucca:
since OLS residual are observed minus predicted values, you should expect that the residuals of your regression models will differ:

use "http://www.stata-press.com/data/r15/auto.dta"

. reg price weight

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(1, 72)        =     29.42
       Model |   184233937         1   184233937   Prob > F        =    0.0000
    Residual |   450831459        72  6261548.04   R-squared       =    0.2901
-------------+----------------------------------   Adj R-squared   =    0.2802
       Total |   635065396        73  8699525.97   Root MSE        =    2502.3

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |   2.044063   .3768341     5.42   0.000     1.292857    2.795268
       _cons |  -6.707353    1174.43    -0.01   0.995     -2347.89    2334.475
------------------------------------------------------------------------------

. estat hettest

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

         chi2(1)      =    13.76
         Prob > chi2  =   0.0002

. reg mpg weight

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(1, 72)        =    134.62
       Model |   1591.9902         1   1591.9902   Prob > F        =    0.0000
    Residual |  851.469256        72  11.8259619   R-squared       =    0.6515
-------------+----------------------------------   Adj R-squared   =    0.6467
       Total |  2443.45946        73  33.4720474   Root MSE        =    3.4389

------------------------------------------------------------------------------
         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |  -.0060087   .0005179   -11.60   0.000    -.0070411   -.0049763
       _cons |   39.44028   1.614003    24.44   0.000     36.22283    42.65774
------------------------------------------------------------------------------

. estat hettest

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

         chi2(1)      =    11.05
         Prob > chi2  =   0.0009

Hence, I would perform two different -estat hettest-.

In addition, as your regression models share the same set of predictors, I woould consider -sureg-:

. sureg (price weight) (mpg weight)

Seemingly unrelated regression
--------------------------------------------------------------------------
Equation             Obs   Parms        RMSE    "R-sq"       chi2        P
--------------------------------------------------------------------------
price                 74       1    2468.262    0.2901      30.24   0.0000
mpg                   74       1      3.3921    0.6515     138.36   0.0000
--------------------------------------------------------------------------

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
price        |
      weight |   2.044063   .3717069     5.50   0.000      1.31553    2.772595
       _cons |  -6.707353    1158.45    -0.01   0.995    -2277.228    2263.813
-------------+----------------------------------------------------------------
mpg          |
      weight |  -.0060087   .0005108   -11.76   0.000    -.0070099   -.0050075
       _cons |   39.44028   1.592043    24.77   0.000     36.31994    42.56063
------------------------------------------------------------------------------

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