Event study with repeated cross section data

[Parul Gupta]

Hello, I am trying to generate an event study graph after running DID regression. My data is a repeated cross-section. The treatment is given all at once in year 2018.
-outcome- variable is the outcome of interest. -rec_treat- identifies the group that receives treatment. -rec_treat*year- is the interaction term (= 1 if received treatment and year>=2018).

The sample data is given below:

* Example generated by -dataex-. For more info, type help dataex
clear
input int(district_code outcome) float(rec_treat year rec_treat*year)
1  8 1 2011 0
1  . 1 2014 0
1  . 1 2013 0
1 42 1 2012 0
1 33 1 2013 0
1 22 1 2012 0
1 22 1 2014 0
1 11 1 2011 0
1 14 1 2011 0
1  3 1 2014 0
1 17 1 2012 0
1  6 1 2014 0
1 18 1 2011 0
1  4 1 2013 0
1 29 1 2014 0
1  6 1 2014 0
1 14 1 2011 0
1 37 1 2011 0
1 19 1 2010 0
1 10 1 2011 0
1 16 1 2010 0
1 11 1 2012 0
1 14 1 2012 0
1 28 1 2010 0
1 25 1 2011 0
1 25 1 2010 0
1  . 1 2014 0
1 23 1 2014 0
1 19 1 2011 0
1 41 1 2011 0
1 26 1 2012 0
1  5 1 2014 0
1 25 1 2010 0
1  9 1 2014 0
1 11 1 2012 0
1 26 1 2014 0
1  5 1 2014 0
1  4 1 2014 0
1  7 1 2010 0
1 29 1 2010 0
1  5 1 2012 0
1  . 1 2014 0
1  9 1 2012 0
1 65 1 2011 0
1 21 1 2011 0
1 34 1 2014 0
1 11 1 2010 0
1  9 1 2014 0
1 20 1 2011 0
1 14 1 2012 0
551  6 1 2022 1
551 12 1 2018 1
551  7 1 2018 1
551  7 1 2022 1
551  8 1 2018 1
551  . 1 2022 1
551  . 1 2022 1
551  6 1 2022 1
551  5 1 2018 1
551 29 1 2018 1
551 24 1 2018 1
551 11 1 2022 1
544  2 1 2022 1
544  8 1 2022 1
544  9 1 2022 1
544  6 1 2018 1
544  9 1 2022 1
544  7 1 2018 1
544 16 1 2022 1
544 12 1 2022 1
544  . 1 2018 1
544 17 1 2018 1
544  3 1 2018 1
544 21 1 2018 1
544  1 1 2022 1
544 17 1 2018 1
544  3 1 2022 1
544 22 1 2022 1
544 10 1 2022 1
544 17 1 2018 1
544  . 1 2022 1
544 14 1 2018 1
544 10 1 2018 1
544  8 1 2018 1
544 11 1 2018 1
544  9 1 2018 1
544 13 1 2018 1
544 26 1 2018 1
544  6 1 2022 1
544  3 1 2018 1
544  7 1 2022 1
544  5 1 2022 1
544 24 1 2018 1
544  9 1 2018 1
544  8 1 2022 1
544  6 1 2022 1
544  6 1 2022 1
544 18 1 2022 1
544  . 1 2018 1
544 10 1 2022 1
544  . 1 2018 1
544 10 1 2022 1
544 19 1 2018 1
544  1 1 2022 1
end

I am using -reghdfe- to run the DD regression and -coefplot- (ssc install ftools) for the event study graph. Please help in generating this.

[Carlo Lazzaro]

Parul:
why not considering -didregress- instead?

[Maxence Morlet]

In addition to Carlo's helpful response, how about ssc install eventdd

[Parul Gupta]

Carlo Lazzaro : I used -didregress- but I am unable to use -ptrends- after that. I get an error saying "treatment times vary", even though all treatment was given in the same period.

Maxence Morlet: I tried that but I get the error "Lead or lag term not found in the range of the event study plot. Ensure that the indicated time var() has full coverage for all leads and lags, or attempt accumulating leads and lags using the accum option." I had created the -time_to_treat- variable as year-2018.


Upon further search, I used the code in https://lost-stats.github.io/Model_E...ent_study.html. I got certain graphs (that look fairly good) but I am unclear how to interpret them. It looks like we are not using the "treated" variable/interaction at all while creating these plots. How does the graph, then, show the difference between the treatment and control groups? Also, what is a desirable graph? Should the coefficients be close to zero or negative before treatment?

Edited to add: I have data for 2010, 2011, 2012, 2014, 2016, 2018 and 2022. Some years are missing. Is this causing failure of ptrends?

[Carlo Lazzaro]

Parul:
there's something wrong in your did specification.
See Example 1 in -didregress- entry, Stata .pdf manual.

[Parul Gupta]

@Carlo: you are probably right. Could you see the following and comment on it pls?

This is how I generate my DID variables:

gen rec_treat= 1 if _m==3 //whether observations are treated is indicated by another data file which I merge with this one
replace rec_treat=0 if _m==1

gen rec_treat*yr=rec_treat*(year>=2018) //treatment year is 2018.

With this specification, estat ptrends does not work.

However, since you mentioned that the DID specification might be incorrect, I redefined the interaction as

gen rec_treat*yr=rec_treat*(year==2018) //treatment year is 2018.

Once I do this, -estat ptrends- works.

However, I wonder if the latter is logical. The treated units continue to benefit from the treatment (the policy was launched in 2018 and is ongoing). So, shouldn't the interaction reflect that the units are still "treated"?

Appreciate your help!

Edited to add: My DID regression is the following:

didregress (outcome) (rec_treat*yr), group(district_code) time(year) vce(cluster district_code)

[Carlo Lazzaro]

Parul:
it seems to me that, in your example, the group are not two, as expected.

[Parul Gupta]

Could you explain further pls? For clarification, I have a household survey. Treatment is given at the district level. My understanding is that there are two groups: treated districts and untreated districts, as required. (All households within the district are assumed to be treated).

Also, when i run didregress, i get the following values for control and treatment times:
control: minimum 2010, maximum 2018
treatment: minimum 2018, maximum 2022 , if I use gen rec_treat*yr=rec_treat*(year>=2018)

Does that help you diagnose the issue better?

I get the error in pretends even I drop the missing values. So it doesn't look like the missing values are causing a problem.

[Parul Gupta]

Correction: In #8, the control units have minimum 2010 and maximum 2022.

[Carlo Lazzaro]

Parul:
in its basic setup, DID needs two groups (treated and control), a treatment, and two time periods (before and after the treatment).
When I code:

. bysort rec_treat_year: tab year if year==2018

Stata returns:

-> rec_treat_year = 0
no observations

-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
-> rec_treat_year = 1

       year |      Freq.     Percent        Cum.
------------+-----------------------------------
       2018 |         27      100.00      100.00
------------+-----------------------------------
      Total |         27      100.00


.

I would expect the control group too to be followed post 2018, to create the counterfactual.

[Parul Gupta]

That's just an issue with the sample data I shared. There are control observations in the full dataset.

[Carlo Lazzaro]

Parul:
could you please share an example of your dataset that that aligns with the DID set up? Thanks.

[Parul Gupta]

Apologies for the delay in response. Here is the data:

clear
input int district_code byte outcome float(rec_treat did year)
20 1 0 0 2012
3 1 0 0 2018
297 . 1 1 2018
2 . 0 0 2011
144 1 0 0 2016
44 1 0 0 2013
34 1 1 0 2012
35 0 0 0 2010
9 1 0 0 2013
8 1 0 0 2011
26 . 0 0 2014
24 1 0 0 2012
13 1 0 0 2013
10 1 0 0 2010
13 . 0 0 2012
29 0 1 0 2012
13 1 0 0 2014
1 . 0 0 2010
19 1 0 0 2013
379 1 0 0 2022
6 1 0 0 2011
529 1 0 0 2022
1 1 0 0 2013
4 1 0 0 2012
5 1 0 0 2010
7 0 0 0 2012
140 1 0 0 2018
22 1 0 0 2014
9 . 0 0 2011
13 1 0 0 2011
13 1 0 0 2011
12 1 0 0 2010
263 1 0 0 2018
37 0 1 0 2010
454 1 0 0 2016
37 0 0 0 2010
3 1 0 0 2016
6 1 0 0 2010
17 1 0 0 2012
102 1 0 0 2018
25 1 0 0 2011
4 1 0 0 2014
13 . 0 0 2014
21 1 0 0 2012
39 1 0 0 2013
8 1 0 0 2010
17 . 0 0 2010
314 1 0 0 2016
16 1 0 0 2014
8 . 0 0 2013
617 1 0 0 2018
63 1 0 0 2012
54 1 0 0 2022
6 0 0 0 2011
9 0 1 0 2014
294 0 0 0 2016
9 0 0 0 2010
18 0 0 0 2010
16 . 0 0 2012
316 1 0 0 2022
345 1 0 0 2018
5 1 0 0 2010
4 0 0 0 2010
18 . 1 0 2010
2 1 1 0 2014
6 0 0 0 2010
15 . 1 0 2010
583 1 0 0 2018
6 0 0 0 2011
5 1 0 0 2010
553 1 0 0 2022
4 1 0 0 2013
4 . 0 0 2011
284 1 0 0 2016
10 . 0 0 2013
24 . 0 0 2010
30 1 0 0 2011
21 1 0 0 2014
1 1 0 0 2011
305 1 0 0 2022
12 1 0 0 2010
21 . 0 0 2013
12 0 0 0 2010
10 1 0 0 2011
16 . 0 0 2010
29 1 1 0 2010
14 1 0 0 2018
4 1 0 0 2012
5 . 1 0 2012
15 1 0 0 2014
394 1 0 0 2018
549 1 0 0 2022
485 1 1 0 2016
571 1 0 0 2016
26 1 1 0 2011
10 . 0 0 2011
289 0 0 0 2022
3 1 1 0 2010
5 0 0 0 2014
4 1 0 0 2010
19 1 0 0 2013
5 0 0 0 2016
284 1 0 0 2022
7 0 1 0 2014
22 1 0 0 2013
479 1 0 0 2022
6 0 0 0 2016
648 1 0 0 2022
19 1 0 0 2013
20 . 1 0 2013
22 0 0 0 2010
11 1 0 0 2012
4 1 0 0 2010
292 0 0 0 2022
422 1 0 0 2018
530 1 0 0 2022
20 1 0 0 2014
6 1 0 0 2013
15 0 1 0 2010
32 0 0 0 2010
19 1 0 0 2012
7 . 0 0 2010
3 1 0 0 2012
3 . 0 0 2016
37 1 0 0 2010
331 1 1 1 2018
6 1 0 0 2013
264 1 0 0 2022
614 . 0 0 2018
281 1 1 1 2022
5 0 1 0 2010
480 1 0 0 2022
21 1 0 0 2014
39 0 0 0 2010
281 1 1 1 2022
1 1 0 0 2011
207 1 0 0 2022
5 0 1 0 2012
485 1 1 0 2016
553 1 0 0 2022
543 1 1 0 2016
17 . 0 0 2011
152 1 0 0 2022
242 1 0 0 2018
13 1 0 0 2014
335 1 0 0 2016
19 0 0 0 2014
23 1 1 0 2014
9 1 0 0 2012
500 1 0 0 2022
3 1 1 0 2011
1 1 0 0 2014
565 1 0 0 2018
561 1 1 1 2018
284 1 0 0 2022
7 1 0 0 2014
63 . 0 0 2010
289 0 0 0 2016
190 1 0 0 2018
6 1 0 0 2011
19 1 0 0 2014
21 1 0 0 2013
4 1 0 0 2012
554 1 0 0 2022
548 1 0 0 2022
9 1 0 0 2012
396 1 0 0 2016
12 1 1 0 2014
113 0 0 0 2018
21 . 0 0 2014
2 1 0 0 2012
21 . 0 0 2010
4 1 0 0 2012
241 1 0 0 2022
9 1 0 0 2013
194 0 0 0 2016
17 . 0 0 2012
220 1 0 0 2018
127 1 0 0 2022
230 1 0 0 2022
2 1 1 0 2010
13 1 0 0 2011
515 1 0 0 2016
9 1 0 0 2013
13 0 0 0 2012
19 0 0 0 2010
279 0 0 0 2016
588 1 0 0 2018
15 1 0 0 2022
601 1 0 0 2018
11 . 0 0 2011
7 0 0 0 2010
8 1 0 0 2011
24 1 0 0 2013
446 0 0 0 2022
20 1 1 0 2012
104 1 0 0 2022
258 1 0 0 2022
37 0 1 0 2010
37 0 0 0 2013
617 1 0 0 2018
9 1 0 0 2012
16 1 0 0 2010
4 1 1 0 2011
30 1 0 0 2014
576 1 0 0 2016
1 0 0 0 2011
28 1 0 0 2013
248 0 0 0 2016
5 1 0 0 2013
1 1 0 0 2010
61 1 0 0 2016
281 1 1 1 2022
658 0 1 1 2022
4 1 0 0 2013
7 1 0 0 2013
4 1 0 0 2012
12 0 1 0 2013
3 1 1 0 2011
3 . 0 0 2012
70 1 0 0 2016
2 1 0 0 2011
548 1 0 0 2022
276 0 0 0 2016
5 1 0 0 2012
23 1 1 0 2016
14 1 0 0 2012
3 1 0 0 2014
552 1 0 0 2022
490 1 0 0 2022
2 0 0 0 2011
6 0 0 0 2010
28 0 0 0 2013
485 1 1 0 2016
9 . 0 0 2011
316 1 0 0 2016
25 0 0 0 2022
421 1 0 0 2018
4 . 0 0 2010
327 1 0 0 2022
601 1 0 0 2022
8 0 0 0 2011
4 1 0 0 2012
27 . 1 0 2010
65 1 0 0 2013
3 1 1 0 2012
594 1 0 0 2018
269 . 0 0 2022
11 1 0 0 2010
578 1 0 0 2022
2 1 0 0 2012
10 1 0 0 2014
250 0 0 0 2022
35 1 0 0 2013
32 1 0 0 2012
186 1 0 0 2018
3 . 0 0 2013
11 1 0 0 2010
35 0 0 0 2010
5 1 0 0 2011
124 1 0 0 2018
4 1 0 0 2012
10 0 0 0 2012
11 1 0 0 2013
251 . 0 0 2016
6 1 0 0 2012
300 1 0 0 2018
5 0 1 0 2010
238 1 1 1 2022
6 . 0 0 2010
9 1 0 0 2011
61 1 0 0 2010
129 1 0 0 2016
19 1 0 0 2010
18 1 0 0 2012
550 1 0 0 2022
241 1 0 0 2018
6 1 0 0 2014
1 1 0 0 2010
13 1 0 0 2010
27 . 0 0 2010
5 0 0 0 2013
2 1 1 0 2014
2 1 0 0 2010
19 1 0 0 2010
502 1 0 0 2018
9 1 0 0 2012
343 1 0 0 2018
3 1 1 0 2014
13 1 0 0 2010
169 1 0 0 2022
6 . 0 0 2010
6 1 0 0 2013
398 1 0 0 2022
7 0 0 0 2011
21 0 1 0 2013
552 1 0 0 2022
8 1 0 0 2010
10 1 0 0 2011
35 1 0 0 2012
9 1 1 0 2012
9 . 1 0 2014
6 1 0 0 2012
610 . 0 0 2018
358 1 1 1 2022
11 1 0 0 2013
15 1 0 0 2022
30 1 0 0 2010
3 1 0 0 2018
8 1 0 0 2014
221 1 0 0 2018
15 1 0 0 2011
553 1 0 0 2022
1 1 0 0 2012
51 1 1 0 2010
512 . 0 0 2022
231 1 0 0 2018
3 1 0 0 2013
9 . 0 0 2014
254 0 0 0 2018
600 1 0 0 2018
269 1 0 0 2016
8 1 0 0 2010
9 0 1 0 2012
5 1 0 0 2012
13 1 0 0 2010
508 1 1 1 2018
521 1 0 0 2022
7 1 0 0 2011
13 0 0 0 2010
19 1 0 0 2012
15 1 0 0 2012
491 1 0 0 2022
21 1 0 0 2012
1 1 0 0 2011
554 1 0 0 2022
520 0 0 0 2018
146 1 0 0 2022
11 1 0 0 2010
3 0 0 0 2012
16 1 0 0 2013
6 . 0 0 2011
1 . 0 0 2011
278 0 0 0 2022
27 1 0 0 2014
101 1 0 0 2018
197 1 0 0 2016
1 1 0 0 2014
13 0 1 0 2011
4 1 0 0 2013
130 1 0 0 2018
244 1 0 0 2022
22 1 0 0 2010
2 1 0 0 2014
3 . 1 0 2012
12 1 0 0 2010
1 0 0 0 2014
34 0 0 0 2010
553 1 0 0 2022
289 1 0 0 2018
24 . 0 0 2010
4 . 0 0 2011
2 0 0 0 2010
23 1 0 0 2011
421 0 0 0 2016
85 1 0 0 2018
42 . 1 1 2018
3 0 0 0 2014
34 1 0 0 2010
482 1 0 0 2016
1 0 0 0 2013
9 . 0 0 2012
18 1 0 0 2010
156 1 0 0 2022
592 1 0 0 2016
25 0 0 0 2022
66 1 1 0 2010
5 1 0 0 2010
20 1 1 0 2012
11 0 0 0 2018
12 1 0 0 2012
40 0 0 0 2010
21 1 0 0 2013
21 1 0 0 2012
6 1 0 0 2012
3 . 0 0 2013
430 1 0 0 2016
1 1 0 0 2014
6 1 0 0 2014
2 1 0 0 2012
4 1 0 0 2011
8 0 0 0 2011
503 1 0 0 2022
8 1 0 0 2013
552 1 0 0 2022
17 1 0 0 2012
221 1 0 0 2022
10 0 0 0 2010
4 1 0 0 2012
244 0 0 0 2022
219 1 0 0 2016
617 1 0 0 2018
3 1 0 0 2014
25 . 0 0 2010
44 1 0 0 2011
11 1 0 0 2013
32 0 0 0 2013
11 1 0 0 2012
633 . 0 0 2018
4 1 0 0 2013
597 1 0 0 2016
269 . 0 0 2018
277 1 0 0 2022
279 1 0 0 2018
4 . 0 0 2013
524 1 0 0 2018
13 1 0 0 2010
4 0 0 0 2014
10 . 0 0 2012
521 1 0 0 2016
592 1 0 0 2016
275 0 0 0 2022
20 1 0 0 2013
15 1 0 0 2010
33 1 0 0 2012
45 1 0 0 2010
554 1 0 0 2022
13 1 0 0 2014
70 1 0 0 2018
8 1 0 0 2011
3 1 0 0 2010
453 1 0 0 2016
7 0 0 0 2010
16 0 0 0 2010
6 1 0 0 2012
22 0 0 0 2010
529 1 0 0 2016
284 0 0 0 2022
6 1 0 0 2013
19 . 0 0 2018
75 1 0 0 2016
10 0 0 0 2012
184 1 1 0 2016
9 1 0 0 2010
9 . 0 0 2011
491 1 0 0 2016
8 . 1 0 2010
555 1 0 0 2022
19 1 0 0 2012
60 1 0 0 2013
21 0 0 0 2013
20 1 0 0 2014
8 0 0 0 2010
28 0 0 0 2012
3 1 0 0 2013
263 1 0 0 2018
13 0 0 0 2014
549 1 0 0 2022
504 1 0 0 2022
68 1 0 0 2010
9 0 1 0 2014
3 1 0 0 2012
5 . 0 0 2011
23 1 0 0 2010
277 0 0 0 2022
15 1 0 0 2011
24 1 0 0 2022
9 1 0 0 2010
454 1 0 0 2016
4 1 1 0 2014
267 0 0 0 2018
15 1 0 0 2014
532 1 0 0 2022
1 . 0 0 2010
9 0 0 0 2013
37 . 0 0 2010
4 1 0 0 2011
6 0 0 0 2010
6 . 0 0 2011
314 . 0 0 2016
483 1 0 0 2016
20 1 0 0 2013
553 1 0 0 2022
38 1 0 0 2012
11 1 0 0 2010
551 1 1 1 2022
13 1 0 0 2013
419 1 0 0 2018
588 1 0 0 2022
8 . 0 0 2010
278 . 0 0 2016
246 1 0 0 2018
9 0 1 0 2010
34 1 0 0 2013
4 0 0 0 2014
278 . 0 0 2016
4 1 0 0 2013
66 1 0 0 2018
24 . 0 0 2011
14 1 0 0 2013
end
[/CODE]

As mentioned in #1, the treatment is given all at once in year 2018.
-outcome- variable is the outcome of interest. -rec_treat- identifies the group that receives treatment. -did- is the interaction term (gen did =0 replace did = 1 if rec_treat==1 & year>=2018).

[Carlo Lazzaro]

Parul:
what about:

. gen After=1 if year>=2018

. replace After=0 if year<2018

. bysort district_code: egen Group=max( rec_treat)

. xtreg outcome c.Group#c.After, fe vce(cluster district_code)

Fixed-effects (within) regression               Number of obs     =        432
Group variable: district_c~e                    Number of groups  =        163

R-squared:                                      Obs per group:
     Within  = 0.0012                                         min =          1
     Between = 0.0017                                         avg =        2.7
     Overall = 0.0046                                         max =         23

                                                F(1, 162)         =      38.08
corr(u_i, Xb) = 0.0239                          Prob > F          =     0.0000

                           (Std. err. adjusted for 163 clusters in district_code)
---------------------------------------------------------------------------------
                |               Robust
        outcome | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
----------------+----------------------------------------------------------------
c.Group#c.After |   .1197605   .0194068     6.17   0.000     .0814377    .1580833
                |
          _cons |   .7828787   .0006738  1161.81   0.000      .781548    .7842093
----------------+----------------------------------------------------------------
        sigma_u |  .31767238
        sigma_e |  .41628541
            rho |  .36802453   (fraction of variance due to u_i)
---------------------------------------------------------------------------------

.

[Parul Gupta]

Thanks, Carlo. Can I use this with -reghdfe- instead of -xtreg- since my data is not a true panel? Further, how can I use this setup for event study/parallel trends?