Standard errors with new -xthdidregress- command in Stata 18

[Noah Blake Smith]

I am trying to understand how -xthdidregress- estimates standard errors for difference-in-differences with two-way fixed effects (TWFE). The help manual suggests standard errors are clustered by treatment level by default. However, using the -regress- command gives me different results. Does anyone know why?

Reproducible example below using a panel of three states from 2001 to 2005. State 1's treatment begins in 2003. The point estimates of interest using -xthdidregress- and -regress- are identical, but their standard errors differ.

clear all

input state year gdp post2003 treatmentGroup treated
1 2001 100 0 1 0
1 2002 115 0 1 0
1 2003 95 1 1 1
1 2004 87 1 1 1
1 2005 73 1 1 1
2 2001 113 0 0 0
2 2002 117 0 0 0
2 2003 121 1 0 0
2 2004 125 1 0 0
2 2005 129 1 0 0
3 2001 47 0 0 0
3 2002 53 0 0 0
3 2003 59 1 0 0
3 2004 62 1 0 0
3 2005 66 1 0 0
end

*Set panel
xtset state year, yearly

*xthdidregress using default VCE

xthdidregress twfe (gdp) (treated), group(state) hettype(time)

note: variable _did_cohort, containing cohort indicators formed by treatment variable treated and group variable state, was added to the dataset.

Computing ATETs using margins ...

Treatment and time information

Time variable: year
Time interval: 2001 to 2005
Control:       _did_cohort = 0
Treatment:     _did_cohort > 0
-------------------------------
                  | _did_cohort
------------------+------------
Number of cohorts |           2
------------------+------------
Number of obs     |
    Never treated |          10
             2003 |           5
-------------------------------

Heterogeneous-treatment-effects regression               Number of obs    = 15
                                                         Number of panels =  3
Estimator:       Two-way fixed effects
Panel variable:  state
Treatment level: state
Control group:   Never treated
Heterogeneity:   Time

                                  (Std. err. adjusted for 3 clusters in state)
------------------------------------------------------------------------------
             |               Robust
        Time |       ATET   std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
        year |
       2003  |        -20   1.984313   -10.08   0.010    -28.53781   -11.46219
       2004  |      -31.5   1.322876   -23.81   0.002    -37.19187   -25.80813
       2005  |      -49.5   1.322876   -37.42   0.001    -55.19187   -43.80813
------------------------------------------------------------------------------

*xthdidregress explicitly specifying default VCE

xthdidregress twfe (gdp) (treated), group(state) hettype(time) vce(cluster state)

note: variable _did_cohort, containing cohort indicators formed by treatment variable treated and group variable state, was added to the dataset.

Computing ATETs using margins ...

Treatment and time information

Time variable: year
Time interval: 2001 to 2005
Control:       _did_cohort = 0
Treatment:     _did_cohort > 0
-------------------------------
                  | _did_cohort
------------------+------------
Number of cohorts |           2
------------------+------------
Number of obs     |
    Never treated |          10
             2003 |           5
-------------------------------

Heterogeneous-treatment-effects regression               Number of obs    = 15
                                                         Number of panels =  3
Estimator:       Two-way fixed effects
Panel variable:  state
Treatment level: state
Control group:   Never treated
Heterogeneity:   Time

                                  (Std. err. adjusted for 3 clusters in state)
------------------------------------------------------------------------------
             |               Robust
        Time |       ATET   std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
        year |
       2003  |        -20   1.984313   -10.08   0.010    -28.53781   -11.46219
       2004  |      -31.5   1.322876   -23.81   0.002    -37.19187   -25.80813
       2005  |      -49.5   1.322876   -37.42   0.001    -55.19187   -43.80813
------------------------------------------------------------------------------

*regress

reg gdp treated#i(2003/2005).year post2003 treatmentGroup i.state i.year, vce(cluster state)

note: 3.state omitted because of collinearity.
note: 2005.year omitted because of collinearity.

Linear regression                               Number of obs     =         15
                                                F(2, 2)           =          .
                                                Prob > F          =          .
                                                R-squared         =     0.9967
                                                Root MSE          =     2.7544

                                    (Std. err. adjusted for 3 clusters in state)
--------------------------------------------------------------------------------
               |               Robust
           gdp | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
  treated#year |
       1 2003  |        -20   2.173707    -9.20   0.012     -29.3527    -10.6473
       1 2004  |      -31.5   1.449138   -21.74   0.002    -37.73514   -25.26486
       1 2005  |      -49.5   1.449138   -34.16   0.001    -55.73514   -43.26486
               |
      post2003 |   19.16667   3.392803     5.65   0.030     4.568614    33.76472
treatmentGroup |       56.8   1.014396    55.99   0.000      52.4354     61.1646
               |
         state |
            2  |       63.6   2.70e-14  2.4e+15   0.000         63.6        63.6
            3  |          0  (omitted)
               |
          year |
         2002  |   8.333333   5.660781     1.47   0.279    -16.02304    32.68971
         2003  |       -7.5   .7245688   -10.35   0.009    -10.61757   -4.382432
         2004  |         -4   2.36e-08 -1.7e+08   0.000           -4          -4
         2005  |          0  (omitted)
               |
         _cons |   46.53333   3.165456    14.70   0.005     32.91348    60.15319
--------------------------------------------------------------------------------

[Enrique Pinzon (StataCorp)]

Dear Noah,

You should get the same results if you exclude i.state from the list of regressors. We use the variable -state- and the treatment variable to form the cohort variable -_did_cohort-. It is the cohort variable that does the work of the treatment group.

Best,

Enrique