Specifying Comparisions in DID models

[Jared Greathouse]

Is it possible in DID regression to compare only certain treated units to certain controls?

Consider this example

net from "https://raw.githubusercontent.com/jgreathouse9/FDIDTutorial/main" net install fdid, replace
  net get fdid, replace
  // Reinstall fdid so you have the most recent version
  clear *
  qui u basque
  // Import basque
  replace treat = 1 if id==12 & year >=1976
  // Pretend Extremadura (a unit that'll never be a donor) was treated
  cls

Suppose I wish to compare Basque only to Cataluna and Aragon, and I only wish to compare Extremadura, I don't know, Andalusia and La Rioja.


Is there any way via the context of a single regression estimator (perhaps using interaction terms?) to specify such a model? I would expect the relevant coefficients to correspond to the DID estimate for each treated unit using ONLY the pre-specified comparison units for each treated unit. Is this something that's readily solvable? Edit: I'm not in the U.S., so I'm away from my laptop, that's why I can't provide any code I've tried myself.

[George Ford]

why wouldn't it be the standard DID model. The issue would be getting sensible SE with so few units and a single treated unit.

[George Ford]

the updated version of fdid is giving me a "variable te not found" error.

I don't see it being created before it's use.

[Andrew Musau]

Is it possible in DID regression to compare only certain treated units to certain controls?

Standard DID is a regular regression model, so that would correspond to estimating each regression separately. Could you estimate them jointly? Yes.

webuse hospdd, clear
didregress (satis) (procedure) if (inrange(hospital, 1, 12)|inrange(hospital, 35, 46)), group(hospital) time(month)
didregress (satis) (procedure) if !(inrange(hospital, 1, 12)|inrange(hospital, 35, 46)), group(hospital) time(month)

gen group1= (inrange(hospital, 1, 12)|inrange(hospital, 35, 46))
xtset hospital
xtreg satis i.group1#(c.procedure i.month) o1.group#o1.month,fe cluster(hospital)

Res.:

. didregress (satis) (procedure) if (inrange(hospital, 1, 12)|inrange(hospital, 35, 46)), group(hospital) time(month)

Treatment and time information

Time variable: month
Control:       procedure = 0
Treatment:     procedure = 1
-----------------------------------
             |   Control  Treatment
-------------+---------------------
Group        |
    hospital |        12         12
-------------+---------------------
Time         |
     Minimum |         1          4
     Maximum |         1          4
-----------------------------------

Difference-in-differences regression                     Number of obs = 4,056
Data type: Repeated cross-sectional

                               (Std. err. adjusted for 24 clusters in hospital)
-------------------------------------------------------------------------------
              |               Robust
        satis | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------+----------------------------------------------------------------
ATET          |
    procedure |
(New vs Old)  |   .8373083   .0416418    20.11   0.000     .7511657     .923451
-------------------------------------------------------------------------------
Note: ATET estimate adjusted for group effects and time effects.

.
. didregress (satis) (procedure) if !(inrange(hospital, 1, 12)|inrange(hospital, 35, 46)), group(hospital) time(month)

Treatment and time information

Time variable: month
Control:       procedure = 0
Treatment:     procedure = 1
-----------------------------------
             |   Control  Treatment
-------------+---------------------
Group        |
    hospital |        16          6
-------------+---------------------
Time         |
     Minimum |         1          4
     Maximum |         1          4
-----------------------------------

Difference-in-differences regression                     Number of obs = 3,312
Data type: Repeated cross-sectional

                               (Std. err. adjusted for 22 clusters in hospital)
-------------------------------------------------------------------------------
              |               Robust
        satis | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------+----------------------------------------------------------------
ATET          |
    procedure |
(New vs Old)  |     .86466      .0502    17.22   0.000     .7602632    .9690567
-------------------------------------------------------------------------------
Note: ATET estimate adjusted for group effects and time effects.

. xtreg satis i.group1#(c.procedure i.month) o1.group#o1.month,fe cluster(hospital)

Fixed-effects (within) regression               Number of obs     =      7,368
Group variable: hospital                        Number of groups  =         46

R-squared:                                      Obs per group:
     Within  = 0.1233                                         min =         88
     Between = 0.1352                                         avg =      160.2
     Overall = 0.1317                                         max =        232

                                                F(14, 45)         =      76.20
corr(u_i, Xb) = 0.0599                          Prob > F          =     0.0000

                                    (Std. err. adjusted for 46 clusters in hospital)
------------------------------------------------------------------------------------
                   |               Robust
             satis | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------------+----------------------------------------------------------------
group1#c.procedure |
                0  |     .86466   .0494247    17.49   0.000     .7651135    .9642064
                1  |   .8373083   .0411018    20.37   0.000      .754525    .9200916
                   |
      group1#month |
       0#February  |  -.0205574   .0328075    -0.63   0.534    -.0866351    .0455204
          0#March  |   .0043268   .0309915     0.14   0.890    -.0580932    .0667469
          0#April  |  -.0147784   .0301772    -0.49   0.627    -.0755585    .0460016
            0#May  |  -.0292926    .032824    -0.89   0.377    -.0954034    .0368183
           0#June  |  -.0109112   .0259441    -0.42   0.676    -.0631653    .0413429
           0#July  |  -.0189196   .0368698    -0.51   0.610    -.0931792      .05534
        1#January  |          0  (omitted)
       1#February  |  -.0006665   .0199154    -0.03   0.973    -.0407781    .0394452
          1#March  |   .0363743   .0209755     1.73   0.090    -.0058726    .0786212
          1#April  |   .0081816   .0320265     0.26   0.800    -.0563231    .0726863
            1#May  |    .008918   .0321917     0.28   0.783    -.0559194    .0737554
           1#June  |   .0040179   .0263931     0.15   0.880    -.0491406    .0571764
           1#July  |  -.0028064   .0288327    -0.10   0.923    -.0608784    .0552656
                   |
             _cons |   3.444675   .0112798   305.39   0.000     3.421956    3.467394
-------------------+----------------------------------------------------------------
           sigma_u |  .66162184
           sigma_e |  .72415904
               rho |  .45496395   (fraction of variance due to u_i)
------------------------------------------------------------------------------------

.

[Jared Greathouse]

George Ford can you post the code that reproduces this issue? I'll look at it on Sunday when I return to Atlanta. Is this a staggered adoption setting or single treatment setup?

[George Ford]

I rebooted and it worked.

It's looking good. Nice work.

[Jared Greathouse]

Thank you! Not done just quite yet, though. Wooldridge sent me his slides on how to do the event study (you know, across cohorts, by using OLS to predict the treatment effect using i.treatment as a predictor, using the bootstrap/exact inference to obtain the standard error for tau by each time period).

The challenging part will be aggregating this up to the ATT across all cohorts. He mentioned to me that to do this yours need to estimate (i think) the intra-cohort covariance matrix to adjust for variability within each cohort. Even the ATT is something of a debate. We could just take the raw empirical average, but Clarke weights the ATT for each cohort by ATT*(number of periods in the cohort/number of periods in the cohort). But even then, there's slight variations we could do, such as Hollingsworth Wing and Freedman who weight by the number of units in each cohort over the total N, among other weights they propose.


Of course, the original question has nada to do with this. I was just trying to see if I could specify the comparison group in the usual way via interaction terms. But either way, thank you, I'm quite happy with the progress. I think extending it to the dynamic setting would make it not just more likely to publish, but more useful for a wider variety of situations, too. George Ford

[George Ford]

Can you borrow from SDID? It generates a period specific se.

[Jared Greathouse]

Yep that's exactly the idea!!! In this case using small N/exact inference. Presumably one could also do placebo inference as SDID does in a similar manner