Staggered Diff-in-Diff

[Mahtab Karimi]

Hi all, I have a quesiotn about staggered DiD and would appreciate your help.

I am running two models about the adoption of two different policies on two different datasets. The treatment group in each model is a set of firms, each firm belongs to only one treatment group.

In both models, I control for time FE, Treatment group FE, and firm FE. My question is why in the first model all Treatment group FE and most of firm FEs will be kept in the model after estimation, but in the second one, all treatment group FEs will be omitted because of collinearity.
The collinearity happens because of the inclusion of firm FE. If it is a matter of collinearity, it must be the same in both cases. Why isn't it? To me, the structure of the model in both cases is exactly the same...

Models are attached below. cik is firms' identifier.

Model 1:

 
. reg Y Dit i.fyear i.Treatment_Group i.cik, vce(cluster cik)

note: 794367.cik omitted because of collinearity.
note: 861884.cik omitted because of collinearity.
note: 907471.cik omitted because of collinearity.
note: 1022079.cik omitted because of collinearity.
note: 1048286.cik omitted because of collinearity.
note: 1059556.cik omitted because of collinearity.
note: 1267238.cik omitted because of collinearity.
note: 1310067.cik omitted because of collinearity.
note: 1341318.cik omitted because of collinearity.
note: 1481792.cik omitted because of collinearity.
note: 1688568.cik omitted because of collinearity.
note: 1944013.cik omitted because of collinearity.

Linear regression                               Number of obs     =      1,170
                                                F(13, 113)        =          .
                                                Prob > F          =          .
                                                R-squared         =     0.8999
                                                Root MSE          =     .09011

                                  (Std. err. adjusted for 114 clusters in cik)
------------------------------------------------------------------------------
             |               Robust
Y            | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         Dit |   .0280684   .0125965     2.23   0.028     .0031124    .0530243
             |
       fyear |
       2011  |  -.0027005   .0091129    -0.30   0.768    -.0207548    .0153539
       2012  |  -.0128803   .0131201    -0.98   0.328    -.0388737     .013113
       2013  |  -.0208039   .0157418    -1.32   0.189    -.0519913    .0103836
       2014  |  -.0127386   .0166187    -0.77   0.445    -.0456633     .020186
       2015  |  -.0176427   .0164005    -1.08   0.284     -.050135    .0148495
       2016  |  -.0158391   .0183057    -0.87   0.389     -.052106    .0204279
       2017  |  -.0099859    .018531    -0.54   0.591    -.0466991    .0267273
       2018  |  -.0109125   .0206403    -0.53   0.598    -.0518045    .0299796
       2019  |  -.0041595   .0199703    -0.21   0.835    -.0437242    .0354052
       2020  |   .0054283   .0201148     0.27   0.788    -.0344228    .0452794
       2021  |  -.0034748   .0226715    -0.15   0.878    -.0483912    .0414415
       2022  |   .0336464   .0554807     0.61   0.545    -.0762708    .1435637
       2023  |   .0835204   .0492043     1.70   0.092    -.0139621    .1810029
             |
Treatment_Group |
       2010  |   .5461846   .0067165    81.32   0.000     .5328781    .5594911
       2011  |   .6583245   .0067165    98.02   0.000      .645018     .671631
       2012  |   .8085951   .0077708   104.06   0.000     .7931996    .8239905
       2013  |    .129572   .0067165    19.29   0.000     .1162654    .1428785
       2014  |   .2153763   .0067165    32.07   0.000     .2020697    .2286828
       2015  |   .5402799   .0067165    80.44   0.000     .5269734    .5535864
       2016  |   .2684022   .0075935    35.35   0.000     .2533582    .2834462
       2017  |   .7142837   .0088295    80.90   0.000     .6967908    .7317766
       2018  |   .6121213   .0075935    80.61   0.000     .5970773    .6271653
       2019  |   .5901068   .0067165    87.86   0.000     .5768002    .6034133
       2020  |  -.0752191   .0079652    -9.44   0.000    -.0909997   -.0594386
       2021  |   .6172731   .0074409    82.96   0.000     .6025313    .6320149
             |
         cik |
       4457  |   .1513102   .0042898    35.27   0.000     .1428114     .159809
       4962  |  -.4800946   .0035268  -136.13   0.000    -.4870818   -.4731074
       7536  |  -.4374177   .0011647  -375.56   0.000    -.4397252   -.4351102
       8670  |   .3191581   .0027083   117.84   0.000     .3137925    .3245237
       8868  |  -.0477404    .009486    -5.03   0.000    -.0665339   -.0289469
       9389  |   .3618816   .0100514    36.00   0.000     .3419678    .3817953
      12927  |    .451338    .001124   401.55   0.000     .4491112    .4535648
      14272  |   .3447496    .006826    50.51   0.000     .3312262    .3582731
     ..................
.....................
   
     789019  |   .4309862    .006826    63.14   0.000     .4174628    .4445097
     794367  |          0  (omitted)
     860748  |   .8515967   .0050526   168.55   0.000     .8415865    .8616069
     861884  |          0  (omitted)
     885639  |  -.3109489   .0069952   -44.45   0.000    -.3248077   -.2970901
     894671  |   .7622711   .0081693    93.31   0.000     .7460862     .778456
     902274  |  -.2795213    .003396   -82.31   0.000    -.2862493   -.2727933
     907471  |          0  (omitted)
       4980  |   .2634658    .001124   234.40   0.000     .2612389    .2656926
    1022079  |          0  (omitted)
    1024478  |   .2228396    .006826    32.65   0.000     .2093161     .236363
    1032208  |  -.0950473    .006826   -13.92   0.000    -.1085708   -.0815239
    1035002  |   .5532175    .006826    81.05   0.000     .5396941     .566741
    1039828  |   .7657814    .006826   112.19   0.000     .7522579    .7793048
    1041061  |    .111915    .006826    16.40   0.000     .0983915    .1254384
    1048286  |          0  (omitted)
    1049782  |   .6380497   .0036464   174.98   0.000     .6308255    .6452738
    1059556  |          0  (omitted)
    1105705  |   .0289986   .0037411     7.75   0.000     .0215868    .0364105
    1122304  |   .2095745   .0059417    35.27   0.000     .1978029    .2213461
    1122976  |  -.3695582   .0054198   -68.19   0.000    -.3802959   -.3588205
    1124198  |   .1101359   .0036464    30.20   0.000     .1029117      .11736
    1135971  |   .7953738   .0128755    61.77   0.000     .7698652    .8208824
    1143068  |   .8521349   .0149329    57.06   0.000     .8225502    .8817197
    1267238  |          0  (omitted)
    1275283  |   .8132747   .0117016    69.50   0.000     .7900916    .8364578
    1310067  |          0  (omitted)
    1326160  |   .1657204   .0047975    34.54   0.000     .1562158    .1752251
    1331875  |  -.1925357   .0047975   -40.13   0.000    -.2020404   -.1830311
    1341318  |          0  (omitted)
    1373835  |   .2368121   .0117016    20.24   0.000      .213629    .2599951
    1378946  |   .5941125   .0077564    76.60   0.000     .5787456    .6094794
    1481792  |          0  (omitted)
    1604028  |   .5350732   .0036464   146.74   0.000     .5278491    .5422973
    1688568  |          0  (omitted)
    1944013  |          0  (omitted)
             |
       _cons |   .1599165   .0190851     8.38   0.000     .1221054    .1977276
------------------------------------------------------------------------------

.

and Model 2:

 
. reg Y Dit  i.fyear i.cik i.Treatment_group , vce(cluster cik)

note: 2000.breachyear omitted because of collinearity.
note: 2006.breachyear omitted because of collinearity.
note: 2007.breachyear omitted because of collinearity.
note: 2008.breachyear omitted because of collinearity.
note: 2010.breachyear omitted because of collinearity.
note: 2011.breachyear omitted because of collinearity.
note: 2012.breachyear omitted because of collinearity.
note: 2013.breachyear omitted because of collinearity.
note: 2014.breachyear omitted because of collinearity.
note: 2015.breachyear omitted because of collinearity.
note: 2016.breachyear omitted because of collinearity.
note: 2017.breachyear omitted because of collinearity.
note: 2018.breachyear omitted because of collinearity.
note: 2019.breachyear omitted because of collinearity.
note: 2020.breachyear omitted because of collinearity.
note: 2021.breachyear omitted because of collinearity.
note: 2022.breachyear omitted because of collinearity.

Linear regression                               Number of obs     =      2,648
                                                F(13, 371)        =          .
                                                Prob > F          =          .
                                                R-squared         =     0.9235
                                                Root MSE          =     .08574

                                  (Std. err. adjusted for 372 clusters in cik)
------------------------------------------------------------------------------
             |               Robust
Y     | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         Dit |   .0261452   .0111887     2.34   0.020      .004144    .0481464
             |
       fyear |
       2011  |   -.016803   .0066192    -2.54   0.012    -.0298189    -.003787
       2012  |  -.0184841   .0071518    -2.58   0.010    -.0325472    -.004421
       2013  |  -.0128866   .0095036    -1.36   0.176    -.0315742     .005801
       2014  |  -.0118556   .0100748    -1.18   0.240    -.0316664    .0079552
       2015  |  -.0117674   .0116588    -1.01   0.313    -.0346931    .0111582
       2016  |   -.012376   .0121683    -1.02   0.310    -.0363036    .0115516
       2017  |  -.0209325   .0128857    -1.62   0.105    -.0462706    .0044057
       2018  |  -.0225738   .0131857    -1.71   0.088    -.0485019    .0033544
       2019  |  -.0260919    .013323    -1.96   0.051      -.05229    .0001062
       2020  |  -.0184946   .0131037    -1.41   0.159    -.0442613    .0072722
       2021  |  -.0379104    .014371    -2.64   0.009    -.0661692   -.0096516
       2022  |   .0400507   .0323113     1.24   0.216    -.0234855    .1035868
       2023  |   .0709154   .0336523     2.11   0.036     .0047422    .1370886
             |
         cik |
       3146  |   .6446921   .0083495    77.21   0.000     .6282738    .6611104
       4281  |  -.2054449   .0009324  -220.34   0.000    -.2072784   -.2036115
       6845  |   .4167743   .0015272   272.89   0.000     .4137712    .4197775
       7084  |  -.0832123   .0023131   -35.98   0.000    -.0877607    -.078664
       7789  |   .6237169   .0039269   158.83   0.000     .6159951    .6314388
       8146  |   .4724508   .0038127   123.92   0.000     .4649536     .479948
       8818  |  -.1622675   .0008506  -190.76   0.000    -.1639402   -.1605948
       8868  |  -.2456957   .0055676   -44.13   0.000    -.2566438   -.2347477
       9092  |   .1093303   .0035347    30.93   0.000     .1023798    .1162808
       9389  |   .1798618   .0035329    50.91   0.000     .1729148    .1868087
       9892  |    -.03082   .0074153    -4.16   0.000    -.0454013   -.0162387
      10795  |   .0053476   .0037296     1.43   0.152    -.0019861    .0126814

   
   ..................................
..................................
.
 ..
.

    1556727  |   .3657087   .0053536    68.31   0.000     .3551814    .3762359
    1571508  |   .6557614   .0088063    74.47   0.000     .6384449     .673078
    1598428  |   .0544575   .0030316    17.96   0.000     .0484962    .0604188
    1602658  |   .5810628   .0037107   156.59   0.000     .5737661    .5883595
    1604028  |   .3623358   .0030316   119.52   0.000     .3563745    .3682971
    1616318  |   .4820546   .0042532   113.34   0.000     .4736912     .490418
    1624794  |   .1532119   .0069113    22.17   0.000     .1396216    .1668021
    1635718  |   .2698516   .0038399    70.28   0.000     .2623009    .2774024
    1636286  |   .6456811   .0055899   115.51   0.000     .6346892     .656673
    1646383  |   .3994345   .0042532    93.91   0.000     .3910711    .4077979
    1666700  |   .0895345    .005811    15.41   0.000     .0781078    .1009612
    1674335  |  -.2330401   .0069113   -33.72   0.000    -.2466304   -.2194498
    1681206  |   .3586259   .0069113    51.89   0.000     .3450356    .3722162
    1688568  |  -.1637423   .0047005   -34.84   0.000    -.1729852   -.1544994
    1711269  |   .5271598   .0053257    98.98   0.000     .5166875     .537632
    1746109  |   .6480332   .0065936    98.28   0.000     .6350678    .6609987
    1750735  |   .6112961   .0065936    92.71   0.000     .5983306    .6242615
    1754226  |   .6160019   .0079011    77.96   0.000     .6004653    .6315385
    1760965  |  -.1186772    .005811   -20.42   0.000    -.1301038   -.1072505
    1766368  |   .5841928   .0121748    47.98   0.000     .5602525    .6081332
    1767837  |   .4929741   .0096057    51.32   0.000     .4740857    .5118626
    1790982  |   -.166308   .0065936   -25.22   0.000    -.1792735   -.1533426
    1849867  |   .4509114   .0156182    28.87   0.000        .4202    .4816227
    1850398  |   .4301086   .0170735    25.19   0.000     .3965356    .4636816
             |
 Treatment_Group|
       2000  |          0  (omitted)
       2006  |          0  (omitted)
       2007  |          0  (omitted)
       2008  |          0  (omitted)
       2010  |          0  (omitted)
       2011  |          0  (omitted)
       2012  |          0  (omitted)
       2013  |          0  (omitted)
       2014  |          0  (omitted)
       2015  |          0  (omitted)
       2016  |          0  (omitted)
       2017  |          0  (omitted)
       2018  |          0  (omitted)
       2019  |          0  (omitted)
       2020  |          0  (omitted)
       2021  |          0  (omitted)
       2022  |          0  (omitted)
             |
       _cons |   .3442386   .0088063    39.09   0.000      .326922    .3615551
------------------------------------------------------------------------------

.

Thank you,
Mahtab

[Jared Greathouse]

Why not just use xtdidregress to solve this problem? I'm sure there's a reason as Stata suggests, but why not use the native command designed for this

[Jeff Wooldridge]

The treatment group is redundant once you have firm fixed effects because a firm can only be treated first at one time period. Stata has rules about which collinear variables are dropped, and it usually drops the last set of collinear variables. Notice how in the first regression, i.cik is last and in the second, i.Treatment_group is last. The problem is easily solved by dropping i.Treatment_group because these are redundant. It won't change you estimate on Dit.

[Mahtab Karimi]

Jeff Wooldridge Thank you so much. That was really helpful. Since you are here, I have one more general question and would appreciate your comment. I come across good papers that control for both industry FE and firm FE. Chances are high in practice one group of those variables will be omitted during estimation. Is it a professional practice to show that the researcher is trying to take account of any unobserved
heterogeneity no matter what happens during estimation? Why do people show both industry and firm FE on the tables?

Thank you,
Mahtab