Difference-in-differences analysis for matched pairs without fixed treatment time

[Holger Reimsbach]

Dear statalist users,

I am examining the effect of the appointment of a chief digital officer at S&P500 companies on strategic change in the company. I am looking at appointments between 2010 and 2019.

I performed a matching of treatment and control firms based on industry (exact matching) and total assets (nearest neighbor).

Now I want to use the matched sample for a difference in differences analysis.

Please find an excerpt of my data below:

* Example generated by -dataex-. For more info, type help dataex
clear
input float matchGroup double PERMCO byte(time treatment) float(interaction sc)
1  1467 1 1 1 -.15027764
1  1467 0 1 0 -.12327062
1 21351 0 0 0 -.11199666
1 21351 1 0 0 -.05841219
4  2551 1 1 1 -.11911808
4  2551 0 1 0 -.10512438
4 36364 1 0 0 -.06052626
4 36364 0 0 0  .20290615
6  3178 1 1 1  -.1839711
6  3178 0 1 0 -.05224591
6  3194 1 0 0 -.04042549
6  3194 0 0 0   .2118327
7  3178 0 1 0 -.17966723
7  3178 1 1 1  -.1585436
7 20834 1 0 0  .04626698
7 20834 0 0 0   .6909865
8  3178 0 1 0 -.16531967
8  3194 1 0 0 -.03260051
8  3194 0 0 0  .04626698
8  3178 1 1 1   .4350691
end

The variable time = 0 refers to the year prior appointment and time = 1 refers to the year after appointment. The variable treatment = 1 if the company belongs to the treatment group, zero otherwise. The variable sc is my dependent variable (a composite measure of strategic change).

There are a few characteristics of my data that differ from the "standard" case:

• The treatment doesn't happen at a fixed time but in any of the years between 2010 and 2019. I am not certain whether this can be treated as I did with assigning a time variable a value of 0 for the year prior appointment and 1 for after appointment. Does this create any methodological issues bc in my case e.g. time = 1 does not refer to the same year?
• How can I incorporate the matching into the analysis? I tried to do to this by -xtset- on my matchGroup variable.
• Some companies in my sample received several treatments. How can this be handled? I ignored this for now.

This is the code I used to implement the DiD analysis:

xtset matchGroup
xtreg sc time##treatment, fe

Do you see any further issues with my approach?

Thanks a lot!

[Holger Reimsbach]

Hi, your help would be highly appreciated. If my question is unclear, please let me know. I am not sure if this is the right approach to implement DiD with my data.

Thanks!