Event Study Plot with DID and Poisson Regression

[Aaradhya Gupta]

Hi all,

I am doing a DID analysis on a legal dataset where each observation is a court case. Every court case has a date of first hearing and date of the decision, and subtracting these gives me my dependent variable 'Days for Decision'. I have an event (a passing of an Act) around which I am looking at the before/after, and sections of the Penal Code that define the treatment/control groups. I am using a poisson regression for this purpose, using the -ppmlhdfe- command.

MWE if required:

* Example generated by -dataex-. For more info, type help dataex
clear
input float hearing_time1 int(court_id section_no) float(timetotreat filing_m_y)
  97 11 304 -19 620
   1 11 337  30 669
   3 11 326  -5 634
  10 11 376  32 671
 456 11 506 -33 606
   3 11 279  64 703
   2 11 406  41 680
 308 11 379  32 671
   3 11 380  58 697
   1 11 506  65 704
  72 11 506  36 675
 191 11 192  19 658
   1 11 452  29 668
   1 11 307  67 706
   1 11 194 -30 609
   4 11 380  34 673
 293 11 407  23 662
  51 11 323  24 663
   2 11  21  -4 635
  29 11 380  27 666
  14 11 506  45 684
   1 11 194  -9 630
   2 11 399  47 686
   2 11 467  55 694
   2 11 323  47 686
   2 11 420  46 685
  63 11 338  32 671
 148 11 304 -16 623
   3 11 379  34 673
   3 11 302  57 696
   2 11 306  63 702
 343 11 506  -9 630
 717 11 506 -21 618
   1 11 420  62 701
   2 11 302  65 704
   1 11 337  56 695
  15 11 307   5 644
  29 11 420  38 677
  15 11 379   8 647
   1 11 354   4 643
  53 11 279  56 695
  30 11 354  33 672
  15 11  34  68 707
   2 11 409  57 696
   1 11 337  23 662
 121 11 337  11 650
 246 11 324  31 670
  15 11 354  60 699
   2 11 511  38 677
  55 11 506  -9 630
 424 11  25 -33 606
   2 11 397  30 669
  38 11 109  19 658
   2 11 394  39 678
   4 11 219 -14 625
  12 11 380  -7 632
   2 11 406  60 699
 169 11 379 -23 616
   1 11 379  53 692
   4 11  34 -21 618
   3 11 379 -14 625
   9 11 506  31 670
 204 11 506  32 671
  30 11 406  50 689
   4 11 379  59 698
   8 11 401  16 655
   1 11 506  15 654
   1 11 506  68 707
  11 11 307  50 689
   3 11 308  57 696
  25 11 302  22 661
  10 11 302  45 684
   1 11 366  27 666
   1 11 379  67 706
  83 11 304  15 654
   1 11 337  36 675
  87 11 379  28 667
   1 11 506  18 657
  15 11 376  37 676
   5 11 498  62 701
1022 11 506  -6 633
   2 11 307  40 679
  81 11 467   5 644
  25 11 325  10 649
 272 11 327 -30 609
   1 11 289  64 703
  70 11 506  68 707
   8 11 354   6 645
   1 11 406  45 684
   1 11 337  12 651
   2 11 467  47 686
  21 11 306  19 658
   1 11 409  62 701
   1 11 506  30 669
  29 11 364  -5 634
   1 11 452  23 662
   1 11 506  19 658
  57 11 279 -11 628
   2 11 324  62 701
   8 11 511 -15 624
end
format %tm filing_m_y

I wanted to make Event Study plots for this data, and am not sure how to do that.

1. I was using the -eventdd- command, but I am not sure if my syntax is correct. I am currently using:

   eventdd hearing_time1 i.court_id i.section_no, timevar(timetotreat) ci(rcap) cluster(section_no)

   where hearing_time1 is my dependent variable, court_id and section_no are court and section fixed effects. The data goes from 2010 till 2018, so timetotreat has been created using by subtracting the month-years from the month of the event (which is 2013m4).
2. Do I need to use the DID coefficient I have created (treatment*post)? Or does the timevar suboption do that already?
3. Additionally, would I need to incorporate Poisson regression in some way, and if so, how would I do that?

I think I am confused about what event study actually does, so advice, guidance, or useful references on any or all of the above would be extremely helpful.