In-time placebo with SDID

[Mohammadamin Firouzi]

Hi everyone,

I'm working with a balanced panel dataset (30 units observed from 1991 to 2015), and I'm using the synthetic control and synthetic difference-in-differences to analyze my data.

I'd like to conduct an in-time placebo test with SDID. Based on "Credible Answers to Hard Questions: Differences-in-Differences for Natural Experiment" by Clément de Chaisemartin and Xavier D’Haultfœuille (page 145), it seems that I should remove the actual treatment year and all subsequent years (my treatment begins in 2008) before running the placebo test. However, I do not understand why this is necessary, since we do not do this when conducting placebo tests in the synthetic control.

I have obtained results both with and without the 2008–2015 period included. Which approach is correct?

Thank you for your help.

local outcomes div divtomarr gdiv

use analysis_sample.dta, clear

tempname results
postfile `results' str10 outcome int year double ATT using sdid_placebo, replace

foreach o of local outcomes {

    qui sdid `o' country_id year treatment, ///
        vce(noinference)

    post `results' ("`o'") (2008) (e(ATT))
}

* drop if year > 2007

foreach y in 2005 2004 2003 2002 2001 {

    capture drop placebo_treatment
    gen placebo_treatment = (country_id == "28" & year >= `y')

    foreach o of local outcomes {

        qui sdid `o' country_id year placebo_treatment, ///
            vce(noinference)

        post `results' ("`o'") (`y') (e(ATT))
    }
}

postclose `results'

use sdid_placebo, clear

rename ATT att

bys outcome: egen actual_att = max(cond(year == 2008, att, .))

gen ratio = actual_att/att if year != 2008

sort outcome year
list outcome year att ratio, sepby(outcome)

With 2008-2015:

    +----------------------------------------+
     |   outcome   year        att      ratio |
     |----------------------------------------|
  1. |       div   2001   .4640257   1.234794 |
  2. |       div   2002   .4630668   1.237351 |
  3. |       div   2003   .5177077   1.106756 |
  4. |       div   2004   .5227098   1.096165 |
  5. |       div   2005   .5501152   1.041556 |
  6. |       div   2008    .572976          . |
     |----------------------------------------|
  7. | divtomarr   2001   .0152673    2.97418 |
  8. | divtomarr   2002   .0189524   2.395881 |
  9. | divtomarr   2003   .0174159   2.607255 |
 10. | divtomarr   2004   .0197184   2.302809 |
 11. | divtomarr   2005   .0154058   2.947442 |
 12. | divtomarr   2008   .0454077          . |
     |----------------------------------------|
 13. |      gdiv   2001   1.074019   1.264214 |
 14. |      gdiv   2002    1.08208   1.254796 |
 15. |      gdiv   2003    1.20649   1.125405 |
 16. |      gdiv   2004   1.297058   1.046823 |
 17. |      gdiv   2005   1.308228   1.037885 |
 18. |      gdiv   2008    1.35779          . |
     +----------------------------------------+

Without 2008-2015:

 
   +------------------------------------------+
     |   outcome   year         att       ratio |
     |------------------------------------------|
  1. |       div   2001    .1162152    4.930302 |
  2. |       div   2002    .0858698    6.672614 |
  3. |       div   2003    .1316963    4.350737 |
  4. |       div   2004    .1323311    4.329866 |
  5. |       div   2005    .1368105    4.188099 |
  6. |       div   2008     .572976           . |
     |------------------------------------------|
  7. | divtomarr   2001   -.0032579   -13.93772 |
  8. | divtomarr   2002   -.0006884   -65.96122 |
  9. | divtomarr   2003   -.0069266   -6.555554 |
 10. | divtomarr   2004   -.0082433   -5.508437 |
 11. | divtomarr   2005   -.0187401   -2.423023 |
 12. | divtomarr   2008    .0454077           . |
     |------------------------------------------|
 13. |      gdiv   2001    .2611531    5.199211 |
 14. |      gdiv   2002    .1743702    7.786824 |
 15. |      gdiv   2003    .2762443    4.915178 |
 16. |      gdiv   2004    .2517797     5.39277 |
 17. |      gdiv   2005    .3174867    4.276683 |
 18. |      gdiv   2008     1.35779           . |
     +------------------------------------------+