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st: regress with vce(robust) and hascons


From   "Michael N. Mitchell" <Michael.Norman.Mitchell@gmail.com>
To   Statalist <statalist@hsphsun2.harvard.edu>
Subject   st: regress with vce(robust) and hascons
Date   Mon, 13 Dec 2010 00:42:32 -0800

Greetings

I am puzzled by the behavior of Stata when I include the -vce(robust)- option along with the -hascons- option.

Consider the example below in which I estimate a model predicting -price- from -foreign- but do so using a cell means model by specifying ibn.foreign and thus include the -hascons- option. I further want robust standard errors so specify the -vce(robust)- option.

. sysuse auto, clear
(1978 Automobile Data)
. regress price ibn.foreign, vce(robust) hascons

Linear regression                                      Number of obs =      74
                                                       F(  2,    72) =  165.64
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.0024
                                                       Root MSE      =  2966.4

------------------------------------------------------------------------------
             |               Robust
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     foreign |
          0  |   6072.423   431.2084    14.08   0.000     5212.825    6932.021
          1  |   6384.682   553.6754    11.53   0.000      5280.95    7488.413
             |
       _cons |  (omitted)
------------------------------------------------------------------------------

The omnibus F test shows 2 degrees of freedom, but I only expected 1 df. The omnibus F test appears to be testing the joint hypothesis that each of the cell means is 0 (see below).

. test 0.foreign 1.foreign

 ( 1)  0bn.foreign = 0
 ( 2)  1.foreign = 0

       F(  2,    72) =  165.64
            Prob > F =    0.0000

But because I specified -hascons- I expect it to test the equality of the cell means. This is the case when I omit the -vce(robust)-, as shown below.

. regress price ibn.foreign, hascons

      Source |       SS       df       MS              Number of obs =      74
-------------+------------------------------           F(  1,    72) =    0.17
       Model |  1507382.66     1  1507382.66           Prob > F      =  0.6802
    Residual |   633558013    72  8799416.85           R-squared     =  0.0024
-------------+------------------------------           Adj R-squared = -0.0115
       Total |   635065396    73  8699525.97           Root MSE      =  2966.4

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     foreign |
          0  |   6072.423    411.363    14.76   0.000     5252.386     6892.46
          1  |   6384.682   632.4346    10.10   0.000     5123.947    7645.417
------------------------------------------------------------------------------

  In this case, the omnibus F test matches the test of the equality of the cell means.

. test 0.foreign = 1.foreign

 ( 1)  0bn.foreign - 1.foreign = 0

       F(  1,    72) =    0.17
            Prob > F =    0.6802

  Perhaps someone can help me understand where I am askew in my thinking about this.

Many thanks,

Michael N. Mitchell
Data Management Using Stata      - http://www.stata.com/bookstore/dmus.html
A Visual Guide to Stata Graphics - http://www.stata.com/bookstore/vgsg.html
Stata tidbit of the week         - http://www.MichaelNormanMitchell.com
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