Significant differences between dummy variables

[Julianna Grato]

I want to test whether the returns to education for workers who are high school graduates are significantly different from returns to education for workers with some college. I ran thsi:

regress loghrwage EDYEARS exper exper2 hsdrop somecollege collegegrad grad

I ran this regression leaving out high school grad as the base group. Do I just look at the result for some college to determine if the returns to education are significantly different? I got a t statistic of 8.01 therefore, I would conclude that they are significantly different?


Thank you.

[David Benson]

Your indicator (dummy) variables are, as you point out, comparing to your omitted group. In this case that was high_school_grad. I always run my regressions several times changing which group is omitted so that I can see "is collegegrad significantly higher than somecollege?", "Is grad significantly higher than collegegrad?, etc

[Phil Bromiley]

You can also directly test the magnitude of the coefficients - while they are relative to the omitted category, you can still test whether they're the same. margins with contrast might also help here.

[Julianna Grato]

Thank you for the feedback. Phil, would "testparm hsgrad somecollege, equal" work? Thank you.

[Rich Goldstein]

I find the question unclear, but maybe the following will help:

. sysuse auto
(1978 Automobile Data)
r; t=0.01 20:59:08

. regress mpg i.rep78

      Source |       SS           df       MS      Number of obs   =        69
-------------+----------------------------------   F(4, 64)        =      4.91
       Model |  549.415777         4  137.353944   Prob > F        =    0.0016
    Residual |  1790.78712        64  27.9810488   R-squared       =    0.2348
-------------+----------------------------------   Adj R-squared   =    0.1869
       Total |   2340.2029        68  34.4147485   Root MSE        =    5.2897

------------------------------------------------------------------------------
         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       rep78 |
          2  |     -1.875   4.181884    -0.45   0.655    -10.22927    6.479274
          3  |  -1.566667   3.863059    -0.41   0.686    -9.284014    6.150681
          4  |   .6666667   3.942718     0.17   0.866    -7.209818    8.543152
          5  |   6.363636   4.066234     1.56   0.123    -1.759599    14.48687
             |
       _cons |         21   3.740391     5.61   0.000     13.52771    28.47229
------------------------------------------------------------------------------
r; t=0.15 20:59:22

. test 2.rep78 = 3.rep78

 ( 1)  2.rep78 - 3.rep78 = 0

       F(  1,    64) =    0.02
            Prob > F =    0.8840
r; t=0.01 20:59:31

. test 2.rep78 = 5.rep78

 ( 1)  2.rep78 - 5.rep78 = 0

       F(  1,    64) =   11.24
            Prob > F =    0.0014

here, I have first tested the coefficient for rep78=2 against the coefficient for rep78=3 and then against the coefficient fore rep78=5

if this kind of test is not what you mean, please clarify

[Julianna Grato]

Yes, thank you so much.