writing the 'didregress'-command as a 'reg'-command

[Emil Alnor]

Hi all

To better understand what is going on in the 'didregress'-command, I want to be able to write it up as a reg-command. I have tried two procedures of doing this. The coefficients obtained are the same as in 'didregress' but the standard errors differ:

use https://www.stata-press.com/data/r17/hospdd, clear

didregress (satis) (procedure), group(hospital) time(month)

*procedure 1
recode hospital (1/18=1 "Treated") (19/46=0 "Control"), gen(treated)
reg satis treated##procedure i.month, vce(cluster hospital)

*procedure 2
recode month (1/3 = 0 "Pre") (4/7 = 1 "Post"), gen(period)
reg satis i.period##i.treated, vce(cluster hospital)

In a previous post Enrique Pinzon (StataCorp) explained that the standard errors in procedure 2 differed because it was a 2-by-2 DiD which differed from the generalized/two-way fixed effect DiD used in 'didregress'. The 'reg' in procedure 1 is my best attempt of writing a generalized DiD, but the standard errors differ from those obtained by 'didregress'. Maybe this is because the standard errors of month is also calculated? Could someone kindly explain how to write the 'didregress' using 'reg'?

[Andrew Musau]

use https://www.stata-press.com/data/r17/hospdd, clear
didregress (satis) (procedure), group(hospital) time(month)
regress satis i.procedure i.hospital i.month, cluster(hospital)

Res.:

. didregress (satis) (procedure), group(hospital) time(month)

Number of groups and treatment time

Time variable: month
Control:       procedure = 0
Treatment:     procedure = 1
-----------------------------------
             |   Control  Treatment
-------------+---------------------
Group        |
    hospital |        28         18
-------------+---------------------
Time         |
     Minimum |         1          4
     Maximum |         1          4
-----------------------------------

Difference-in-differences regression                     Number of obs = 7,368
Data type: Repeated cross-sectional

                               (Std. err. adjusted for 46 clusters in hospital)
-------------------------------------------------------------------------------
              |               Robust
        satis | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------+----------------------------------------------------------------
ATET          |
    procedure |
(New vs Old)  |   .8479879   .0321121    26.41   0.000     .7833108     .912665
-------------------------------------------------------------------------------
Note: ATET estimate adjusted for group effects and time effects.

. 
. regress satis i.procedure i.hospital i.month, cluster(hospital)

Linear regression                               Number of obs     =      7,368
                                                F(6, 45)          =          .
                                                Prob > F          =          .
                                                R-squared         =     0.5333
                                                Root MSE          =     .72384

                              (Std. err. adjusted for 46 clusters in hospital)
------------------------------------------------------------------------------
             |               Robust
       satis | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   procedure |
        New  |   .8479879   .0321121    26.41   0.000     .7833108     .912665
             |
    hospital |
          2  |   .4085664   2.43e-14  1.7e+13   0.000     .4085664    .4085664
          3  |   .5336248   2.43e-14  2.2e+13   0.000     .5336248    .5336248
          4  |   .2275102   2.43e-14  9.4e+12   0.000     .2275102    .2275102
          5  |  -.1453529   2.43e-14 -6.0e+12   0.000    -.1453529   -.1453529
          6  |   .4478634   2.43e-14  1.8e+13   0.000     .4478634    .4478634
          7  |   1.404416   2.46e-14  5.7e+13   0.000     1.404416    1.404416
          8  |   .0718758   2.43e-14  3.0e+12   0.000     .0718758    .0718758
          9  |  -1.518515   2.43e-14 -6.2e+13   0.000    -1.518515   -1.518515
         10  |   1.682845   2.44e-14  6.9e+13   0.000     1.682845    1.682845
         11  |   .2209653   2.43e-14  9.1e+12   0.000     .2209653    .2209653
         12  |  -.0953034   2.43e-14 -3.9e+12   0.000    -.0953034   -.0953034
         13  |   .4955931   2.43e-14  2.0e+13   0.000     .4955931    .4955931
         14  |   .2330426   2.43e-14  9.6e+12   0.000     .2330426    .2330426
         15  |  -.1444935   2.43e-14 -5.9e+12   0.000    -.1444935   -.1444935
         16  |   1.414268   2.43e-14  5.8e+13   0.000     1.414268    1.414268
         17  |   .4235429   2.43e-14  1.7e+13   0.000     .4235429    .4235429
         18  |   .1532761   2.43e-14  6.3e+12   0.000     .1532761    .1532761
         19  |  -.7453017   .0160561   -46.42   0.000    -.7776403   -.7129632
         20  |   .0473874   .0160561     2.95   0.005     .0150489     .079726
         21  |   1.194337   .0160561    74.39   0.000     1.161998    1.226676
         22  |   .7993153   .0160561    49.78   0.000     .7669768    .8316539
         23  |   .7017202   .0160561    43.70   0.000     .6693817    .7340588
         24  |   -.308126   .0160561   -19.19   0.000    -.3404646   -.2757875
         25  |   .6464736   .0160561    40.26   0.000     .6141351    .6788122
         26  |   .2142471   .0160561    13.34   0.000     .1819086    .2465857
         27  |  -.3986544   .0160561   -24.83   0.000     -.430993   -.3663159
         28  |   .7119953   .0160561    44.34   0.000     .6796568    .7443339
         29  |   .2485512   .0160561    15.48   0.000     .2162127    .2808898
         30  |   -.167922   .0160561   -10.46   0.000    -.2002606   -.1355835
         31  |   .5120848   .0160561    31.89   0.000     .4797462    .5444233
         32  |  -.3233456   .0160561   -20.14   0.000    -.3556842   -.2910071
         33  |  -.4539752   .0160561   -28.27   0.000    -.4863137   -.4216366
         34  |  -.0004123   .0160561    -0.03   0.980    -.0327509    .0319262
         35  |    .354111   .0160561    22.05   0.000     .3217724    .3864495
         36  |   2.138142   .0160561   133.17   0.000     2.105804    2.170481
         37  |   .1404036   .0160561     8.74   0.000      .108065    .1727421
         38  |   -.086806   .0160561    -5.41   0.000    -.1191445   -.0544674
         39  |  -.0234969   .0160561    -1.46   0.150    -.0558355    .0088416
         40  |   1.121533   .0160561    69.85   0.000     1.089195    1.153872
         41  |  -.1497346   .0160561    -9.33   0.000    -.1820731    -.117396
         42  |   .8811369   .0160561    54.88   0.000     .8487984    .9134755
         43  |  -.7724325   .0160561   -48.11   0.000    -.8047711    -.740094
         44  |    .034412   .0160561     2.14   0.038     .0020735    .0667506
         45  |  -.2137495   .0160561   -13.31   0.000     -.246088   -.1814109
         46  |   .0784915   .0160561     4.89   0.000     .0461529      .11083
             |
       month |
   February  |  -.0096077   .0184317    -0.52   0.605    -.0467311    .0275158
      March  |   .0219686    .018251     1.20   0.235    -.0147907    .0587279
      April  |  -.0032839   .0221028    -0.15   0.883    -.0478013    .0412335
        May  |  -.0094027   .0232399    -0.40   0.688    -.0562103    .0374048
       June  |  -.0038375   .0190634    -0.20   0.841    -.0422332    .0345581
       July  |  -.0111941   .0230029    -0.49   0.629    -.0575244    .0351361
             |
       _cons |   3.171657   .0172328   184.05   0.000     3.136948    3.206365
------------------------------------------------------------------------------

.

[Emil Alnor]

Thanks, Andrew Musau !