T-test of difference between two regression coefficients within same model

[Stini Berg]

Hello,

I have one single regression model estimating the coefficients (b) of two independent variables (both are binary dummy variables).
After the regression, I would like to do a t-test which calculates the difference between the two variables' coefficients (bIV1 - bIV2) and then gives a p-value for that (i.e. p-value: bIV1 = bIV2).

Can anyone help me how to do that?

[Andrew Musau]

The test of difference between coefficients is a Wald test. See

help test

[Carlo Lazzaro]

Stini:
this is a job for -lincom-:

. use "C:\Program Files\Stata16\ado\base\a\auto.dta"
(1978 Automobile Data)

. regress price i.foreign i.rep78

      Source |       SS           df       MS      Number of obs   =        69
-------------+----------------------------------   F(5, 63)        =      0.19
       Model |  8372481.37         5  1674496.27   Prob > F        =    0.9670
    Residual |   568424478        63  9022610.75   R-squared       =    0.0145
-------------+----------------------------------   Adj R-squared   =   -0.0637
       Total |   576796959        68  8482308.22   Root MSE        =    3003.8

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     foreign |
    Foreign  |    36.7572   1010.484     0.04   0.971    -1982.533    2056.048
             |
       rep78 |
          2  |   1403.125   2374.686     0.59   0.557    -3342.306    6148.556
          3  |   1861.058   2195.967     0.85   0.400    -2527.232    6249.347
          4  |   1488.621   2295.176     0.65   0.519    -3097.921    6075.164
          5  |   1318.426   2452.565     0.54   0.593    -3582.634    6219.485
             |
       _cons |     4564.5   2123.983     2.15   0.035     320.0579    8808.942
------------------------------------------------------------------------------

. mat list e(b)

e(b)[1,8]
           0b.         1.        1b.         2.         3.         4.         5.           
      foreign    foreign      rep78      rep78      rep78      rep78      rep78      _cons
y1          0  36.757202          0   1403.125  1861.0576  1488.6214  1318.4259     4564.5

. lincom 1.foreign-1b.rep78

 ( 1)  1.foreign - 1b.rep78 = 0

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         (1) |    36.7572   1010.484     0.04   0.971    -1982.533    2056.048
------------------------------------------------------------------------------

[Leonardo Guizzetti]

Andrew provided excellent advice. -test- will simply report the Wald test statistic and associated p-value. If you wanted to see magnitude (and confidence interval) of the difference of those coefficients, then -lincom- is an equivalent approach.

help lincom

Edit: crossed with #3 which demonstrates lincom.

[Stini Berg]

Carlo, this was great advice! Thank you very much!