Margins and coefficient differences in marginal effects between two regression variables

[Asad Rind]

I am running following regression model:

probit f.audit fnedpro_bx_w fedpro_bx_w lnbs_w nedpro_bx_w lnbm_w ceo_chair csr_com sustain_comp rd_int_w cap_int_w roa3_w tq_w cash_ta_w lev_w size_w i.year i.sic3 i.cnt

After the regression, i wanted to calculate the margins for two variables 'fnedpro_bx_w fedpro_bx_w' and run the following classical margin command

margins, dydx(fnedpro_bx_w fedpro_bx_w)

The output is

now, i want to calculate whether the difference between these marginal effects is significant. How can I proceed?

[Carlo Lazzaro]

Asad:
I do hope that what follows can help:

. use "C:\Program Files\Stata17\ado\base\a\auto.dta"
(1978 automobile data)

. probit foreign price i.rep78

note: 1.rep78 != 0 predicts failure perfectly;
      1.rep78 omitted and 2 obs not used.

note: 2.rep78 != 0 predicts failure perfectly;
      2.rep78 omitted and 8 obs not used.

note: 5.rep78 omitted because of collinearity.
Iteration 0:   log likelihood = -38.411464  
Iteration 1:   log likelihood = -27.497592  
Iteration 2:   log likelihood = -27.443743  
Iteration 3:   log likelihood = -27.443712  
Iteration 4:   log likelihood = -27.443712  

Probit regression                                       Number of obs =     59
                                                        LR chi2(3)    =  21.94
                                                        Prob > chi2   = 0.0001
Log likelihood = -27.443712                             Pseudo R2     = 0.2855

------------------------------------------------------------------------------
     foreign | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       price |  -3.37e-06   .0000771    -0.04   0.965    -.0001545    .0001477
             |
       rep78 |
          1  |          0  (empty)
          2  |          0  (empty)
          3  |  -2.188324   .5409016    -4.05   0.000    -3.248472   -1.128176
          4  |  -.9070661   .5309678    -1.71   0.088    -1.947744    .1336117
          5  |          0  (omitted)
             |
       _cons |   .9275355   .6200561     1.50   0.135    -.2877522    2.142823
------------------------------------------------------------------------------

. margin rep78

Predictive margins                                          Number of obs = 59
Model VCE: OIM

Expression: Pr(foreign), predict()

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       rep78 |
          3  |   .0999719   .0547964     1.82   0.068     -.007427    .2073709
          4  |   .4997956   .1179251     4.24   0.000     .2686666    .7309245
          5  |   .8176674    .117021     6.99   0.000     .5883105    1.047024
------------------------------------------------------------------------------

. mat list r(b)

r(b)[1,3]
            3.         4.         5.
        rep78      rep78      rep78
r1  .09997193  .49979557   .8176674

. test 3.rep78=4.rep78

 ( 1)  [foreign]3.rep78 - [foreign]4.rep78 = 0

           chi2(  1) =    8.88
         Prob > chi2 =    0.0029

[Asad Rind]

Thanks alot Carlo Lazzaro. It worked. A follow-up question is how can one compare the coefficients of the margins from two different probit models. for example i run two following models based on absence and presence of sensitive industry

 
 probit f.audit fem_pro_bx_w lnbs_w nedpro_bx_w lnbm_w ceo_chair csr_com sustain_comp rd_int_w cap_int_w roa3_w tq_w cash_ta_w lev_w size_w i.year i.sic3 i.cnt if sensitive==1

&

 
 probit f.audit fem_pro_bx_w lnbs_w nedpro_bx_w lnbm_w ceo_chair csr_com sustain_comp rd_int_w cap_int_w roa3_w tq_w cash_ta_w lev_w size_w i.year i.sic3 i.cnt if sensitive==0

I can calculate the margins from both models through the margins command and store them using

eststo margin: margins, dydx(fem_pro_bx_w) post

, however, I am not able to calculate the difference between these two stored margins.

[Carlo Lazzaro]

Asas:
two comments:
1) I would consider one -probit- regression only and include -i.sensitive- as a predictor. Then go -margins-;
2) I would forget -margins- and consider -suest- if you want to stick wity the two-equation framework.