Using eydx to calculate percentage difference in Y in difference-in-difference-analysis for men and women

[Gustav Egede Hansen]

Hi everybody

I am conducting a DID-analysis. Among other things, I am looking to see how a treatment impacts the salary for men and women. However, just comparing the coefficient tells only half of the story. I also need to take into account the baseline salary for men and women.
Therefore, I have been looking into using – margins, eydx - to calculate percentage difference in y for a difference in treatment (0 1) for men and women. I would like to know whether or not this is a correct approach.

Here is some coding and some example data. In the data, men and women experience the same decline of 5000 but the eydx provides the two different percentage decreases, respectively 12.5% for men and 16.6% for women. This all seems very logical to me (and maybe this questions is redundant).

* For men
reg salary i.time##i.treatment##i.gender 
            margins treatment, at(time=(97 98 99 101 102 103) gender =(0))
            marginsplot            

qui reg salary i.time##i.treatment##i.gender       
            margins treatment, at(time=(99 101) gender =(0))             
            margins, eydx(treatment) at(time=(99 101) gender =(0)) post    
            margins, coeflegend    
            di (exp(_b[1.treatment:2._at])-1)*100 

* women
reg salary i.time##i.treatment##i.gender 
            margins treatment, at(time=(97 98 99 101 102 103) gender =(1))
            marginsplot            
                        
qui reg salary i.time##i.treatment##i.gender  
            margins treatment, at(time=(99 101) gender =(1))     
            margins, eydx(treatment) at(time=(99 101) gender =(1)) post 
            margins, coeflegend 
            di (exp(_b[1.treatment:2._at])-1)*100

* Example generated by -dataex-. For more info, type help dataex
clear
input float(id time treatment salary gender)
 1  97 1 30000 1
 1  98 1 30000 1
 1  99 1 30000 1
 1 100 1 30000 1
 1 101 1 25000 1
 1 102 1 25000 1
 1 103 1 25000 1
 2  97 1 30000 1
 2  98 1 30000 1
 2  99 1 30000 1
 2 100 1 30000 1
 2 101 1 25000 1
 2 102 1 25000 1
 2 103 1 25000 1
 5  97 1 40000 0
 5  98 1 40000 0
 5  99 1 40000 0
 5 100 1 40000 0
 5 101 1 35000 0
 5 102 1 35000 0
 5 103 1 35000 0
 6  97 0 30000 1
 6  98 0 30000 1
 6  99 0 30000 1
 6 100 0 30000 1
 6 101 0 30000 1
 6 102 0 30000 1
 6 103 0 30000 1
 7  97 0 30000 1
 7  98 0 30000 1
 7  99 0 30000 1
 7 100 0 30000 1
 7 101 0 30000 1
 7 102 0 30000 1
 7 103 0 30000 1
 8  97 0 40000 0
 8  98 0 40000 0
 8  99 0 40000 0
 8 100 0 40000 0
 8 101 0 40000 0
 8 102 0 40000 0
 8 103 0 40000 0
 9  97 0 40000 0
 9  98 0 40000 0
 9  99 0 40000 0
 9 100 0 40000 0
 9 101 0 40000 0
 9 102 0 40000 0
 9 103 0 40000 0
12  97 1 40000 0
12  98 1 40000 0
12  99 1 40000 0
12 100 1 40000 0
12 101 1 35000 0
12 102 1 35000 0
12 103 1 35000 0
13  97 0 40000 0
13  98 0 40000 0
13  99 0 40000 0
13 100 0 40000 0
13 101 0 40000 0
13 102 0 40000 0
13 103 0 40000 0
14  97 0 40000 0
14  98 0 40000 0
14  99 0 40000 0
14 100 0 40000 0
14 101 0 40000 0
14 102 0 40000 0
14 103 0 40000 0
15  97 0 30000 1
15  98 0 30000 1
15  99 0 30000 1
15 100 0 30000 1
15 101 0 30000 1
15 102 0 30000 1
15 103 0 30000 1
16  97 0 30000 1
16  98 0 30000 1
16  99 0 30000 1
16 100 0 30000 1
16 101 0 30000 1
16 102 0 30000 1
16 103 0 30000 1
17  97 1 40000 0
17  98 1 40000 0
17  99 1 40000 0
17 100 1 40000 0
17 101 1 35000 0
17 102 1 35000 0
17 103 1 35000 0
18  97 1 40000 0
18  98 1 40000 0
18  99 1 40000 0
18 100 1 40000 0
18 101 1 35000 0
18 102 1 35000 0
18 103 1 35000 0
19  97 1 30000 1
19  98 1 30000 1
end