xthdidregress vs csdid

[Hwanseong Pak]

Hello,
I am investigating the effect of a environmental policy on corporate innovation (patents, r&d expenditure). There are 3 phases, and the treatment sometimes stops at phase 1, 2 for some firms(very few).
I am deciding whether to remove those firms and run xthdidregress for staggered effect or csdid. I have experience with using xthdidregress but not csdid. I am studying csdid, but I am not really understanding it. I especially do not understand how to setup gvar (treatment group identifier) in the syntax below:.
csdid depvar [indepvars] [if] [in] [weight], [ivar(varname)] time(varname) gvar(varname) [ options ]
My current treatment varialbe looks as follows:

Firm / Year / Treatment
A 2012 0

A 2013 0

A 2014 0

A 2015 1

......

A 2020 1

A 2021 0

A 2022 0

A 2023 0



Can someone explain what the gvar(varname) is supposed to be and how to chang my current treatment variable to fit the syntax?

Kind regards,
Pak

[Pei-Chun Lai]

Hi Hwanseong,

Please read the following comparison:

. use https://www.stata-press.com/data/r18/akc, clear
(Fictional dog breed and AKC registration data)

. xtset breed year

Panel variable: breed (strongly balanced)
 Time variable: year, 2031 to 2040
         Delta: 1 unit

. *-xthdidregress ra- vs -csdid, method(reg)-
. xthdidregress ra (registered best) (movie), group(breed)  ///
>         cohortvar(cohort, replace) nolog
note: variable cohort, containing cohort indicators formed by treatment variable movie and group variable breed, was added to the dataset.

Treatment and time information

Time variable: year
Time interval: 2031 to 2040
Control:       cohort = 0
Treatment:     cohort > 0
-----------------------------
                  |    cohort
------------------+----------
Number of cohorts |         4
------------------+----------
Number of obs     |
    Never treated |      1190
             2034 |        40
             2036 |        30
             2037 |       150
-----------------------------

Heterogeneous-treatment-effects regression            Number of obs    = 1,410
                                                      Number of panels =   141
Estimator:       Regression adjustment
Panel variable:  breed
Treatment level: breed
Control group:   Never treated

                                (Std. err. adjusted for 141 clusters in breed)
------------------------------------------------------------------------------
             |               Robust
Cohort       |       ATET   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
2034         |
        year |
       2032  |  -254.8927   266.1024    -0.96   0.338    -776.4439    266.6584
       2033  |  -257.5329   217.9389    -1.18   0.237    -684.6852    169.6194
       2034  |   701.1318   127.0935     5.52   0.000     452.0331    950.2304
       2035  |   1099.044   282.0704     3.90   0.000      546.196    1651.892
       2036  |   1367.632   225.8702     6.05   0.000     924.9343    1810.329
       2037  |   2008.294   237.2396     8.47   0.000     1543.313    2473.275
       2038  |   2472.624   278.2949     8.88   0.000     1927.176    3018.072
       2039  |   2689.615   504.3324     5.33   0.000     1701.142    3678.088
       2040  |    3110.97    568.916     5.47   0.000     1995.915    4226.025
-------------+----------------------------------------------------------------
2036         |
        year |
       2032  |   216.0259   122.9107     1.76   0.079    -24.87472    456.9265
       2033  |  -172.5154   372.0776    -0.46   0.643    -901.7741    556.7433
       2034  |  -218.0495   504.5267    -0.43   0.666    -1206.904    770.8045
       2035  |    621.033   156.1306     3.98   0.000     315.0227    927.0434
       2036  |   999.0781   180.1055     5.55   0.000     646.0779    1352.078
       2037  |   1003.333   250.5916     4.00   0.000     512.1829    1494.484
       2038  |   1556.669   451.6914     3.45   0.001     671.3697    2441.967
       2039  |   2590.674   662.6979     3.91   0.000      1291.81    3889.538
       2040  |   2225.712   486.9917     4.57   0.000     1271.225    3180.198
-------------+----------------------------------------------------------------
2037         |
        year |
       2032  |   -114.582   160.0972    -0.72   0.474    -428.3668    199.2028
       2033  |  -127.9856   183.3941    -0.70   0.485    -487.4315    231.4603
       2034  |   33.40901   168.0312     0.20   0.842    -295.9262    362.7442
       2035  |   130.3495   166.2261     0.78   0.433    -195.4477    456.1468
       2036  |  -10.48288   167.5059    -0.06   0.950    -338.7884    317.8226
       2037  |   1717.016   268.5592     6.39   0.000      1190.65    2243.383
       2038  |   2086.798   278.0215     7.51   0.000     1541.886     2631.71
       2039  |   2473.611    268.186     9.22   0.000     1947.976    2999.246
       2040  |   2835.117   378.6699     7.49   0.000     2092.938    3577.296
------------------------------------------------------------------------------
Note: ATET computed using covariates.
Note: Base time for pretreatment ATETs is the previous period.

. csdid registered best, ivar(breed) time(year) gvar(cohort) method(reg)
...........................
Difference-in-difference with Multiple Time Periods

                                                         Number of obs = 1,410
Outcome model  : regression adjustment
Treatment model: none
------------------------------------------------------------------------------
             | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
g2034        |
 t_2031_2032 |  -254.8927   266.1024    -0.96   0.338    -776.4439    266.6584
 t_2032_2033 |  -257.5329   217.9389    -1.18   0.237    -684.6852    169.6194
 t_2033_2034 |   701.1318   127.0935     5.52   0.000     452.0331    950.2304
 t_2033_2035 |   1099.044   282.0704     3.90   0.000      546.196    1651.892
 t_2033_2036 |   1367.632   225.8702     6.05   0.000     924.9343    1810.329
 t_2033_2037 |   2008.294   237.2396     8.47   0.000     1543.313    2473.275
 t_2033_2038 |   2472.624   278.2949     8.88   0.000     1927.176    3018.072
 t_2033_2039 |   2689.615   504.3324     5.33   0.000     1701.142    3678.088
 t_2033_2040 |    3110.97    568.916     5.47   0.000     1995.915    4226.025
-------------+----------------------------------------------------------------
g2036        |
 t_2031_2032 |   216.0259   122.9107     1.76   0.079    -24.87472    456.9265
 t_2032_2033 |  -172.5154   372.0776    -0.46   0.643    -901.7741    556.7433
 t_2033_2034 |  -218.0495   504.5267    -0.43   0.666    -1206.904    770.8045
 t_2034_2035 |    621.033   156.1306     3.98   0.000     315.0227    927.0434
 t_2035_2036 |   999.0781   180.1055     5.55   0.000     646.0779    1352.078
 t_2035_2037 |   1003.333   250.5916     4.00   0.000     512.1829    1494.484
 t_2035_2038 |   1556.669   451.6914     3.45   0.001     671.3697    2441.967
 t_2035_2039 |   2590.674   662.6979     3.91   0.000      1291.81    3889.538
 t_2035_2040 |   2225.712   486.9917     4.57   0.000     1271.225    3180.198
-------------+----------------------------------------------------------------
g2037        |
 t_2031_2032 |   -114.582   160.0972    -0.72   0.474    -428.3668    199.2028
 t_2032_2033 |  -127.9856   183.3941    -0.70   0.485    -487.4315    231.4603
 t_2033_2034 |   33.40901   168.0312     0.20   0.842    -295.9262    362.7442
 t_2034_2035 |   130.3495   166.2261     0.78   0.433    -195.4477    456.1468
 t_2035_2036 |  -10.48288   167.5059    -0.06   0.950    -338.7884    317.8226
 t_2036_2037 |   1717.016   268.5592     6.39   0.000      1190.65    2243.383
 t_2036_2038 |   2086.798   278.0215     7.51   0.000     1541.886     2631.71
 t_2036_2039 |   2473.611    268.186     9.22   0.000     1947.976    2999.246
 t_2036_2040 |   2835.117   378.6699     7.49   0.000     2092.938    3577.296
------------------------------------------------------------------------------
Control: Never Treated

See Callaway and Sant'Anna (2021) for details

. 
. *-xthdidregress aipw- vs -csdid, method(dripw)-
. xthdidregress aipw (registered best) (movie best), group(breed)  ///
>          cohortvar(cohort, replace) nolog
note: variable cohort, containing cohort indicators formed by treatment variable movie and group variable breed, was added to the dataset.

Treatment and time information

Time variable: year
Time interval: 2031 to 2040
Control:       cohort = 0
Treatment:     cohort > 0
-----------------------------
                  |    cohort
------------------+----------
Number of cohorts |         4
------------------+----------
Number of obs     |
    Never treated |      1190
             2034 |        40
             2036 |        30
             2037 |       150
-----------------------------

Heterogeneous-treatment-effects regression            Number of obs    = 1,410
                                                      Number of panels =   141
Estimator:       Augmented IPW
Panel variable:  breed
Treatment level: breed
Control group:   Never treated

                                (Std. err. adjusted for 141 clusters in breed)
------------------------------------------------------------------------------
             |               Robust
Cohort       |       ATET   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
2034         |
        year |
       2032  |  -254.8927   266.1024    -0.96   0.338    -776.4439    266.6584
       2033  |  -257.5329   217.9389    -1.18   0.237    -684.6852    169.6194
       2034  |   701.1318   127.0935     5.52   0.000     452.0331    950.2305
       2035  |   1099.044   282.0704     3.90   0.000      546.196    1651.892
       2036  |   1367.632   225.8702     6.05   0.000     924.9343    1810.329
       2037  |   2008.294   237.2396     8.47   0.000     1543.313    2473.275
       2038  |   2472.624   278.2949     8.88   0.000     1927.176    3018.072
       2039  |   2689.615   504.3324     5.33   0.000     1701.142    3678.088
       2040  |    3110.97    568.916     5.47   0.000     1995.915    4226.024
-------------+----------------------------------------------------------------
2036         |
        year |
       2032  |   216.0259   122.9107     1.76   0.079    -24.87472    456.9265
       2033  |  -172.5154   372.0776    -0.46   0.643    -901.7741    556.7433
       2034  |  -218.0495   504.5267    -0.43   0.666    -1206.904    770.8046
       2035  |    621.033   156.1306     3.98   0.000     315.0227    927.0433
       2036  |   999.0781   180.1055     5.55   0.000     646.0779    1352.078
       2037  |   1003.333   250.5916     4.00   0.000     512.1829    1494.484
       2038  |   1556.668   451.6914     3.45   0.001     671.3697    2441.967
       2039  |   2590.674   662.6979     3.91   0.000      1291.81    3889.538
       2040  |   2225.712   486.9917     4.57   0.000     1271.225    3180.198
-------------+----------------------------------------------------------------
2037         |
        year |
       2032  |   -121.857   159.0273    -0.77   0.444    -433.5448    189.8307
       2033  |  -136.1117   182.3992    -0.75   0.456    -493.6076    221.3843
       2034  |   35.53022   166.7673     0.21   0.831    -291.3276    362.3881
       2035  |   138.6257   164.9303     0.84   0.401    -184.6318    461.8832
       2036  |  -11.14846   166.5179    -0.07   0.947    -337.5176    315.2207
       2037  |   1826.033   268.0048     6.81   0.000     1300.753    2351.313
       2038  |   2219.293   277.3226     8.00   0.000     1675.751    2762.836
       2039  |   2630.665   267.4985     9.83   0.000     2106.378    3154.953
       2040  |   3015.125    378.255     7.97   0.000     2273.758    3756.491
------------------------------------------------------------------------------
Note: ATET computed using covariates.
Note: Base time for pretreatment ATETs is the previous period.

. csdid registered best, ivar(breed) time(year) ///
>         gvar(cohort) method(dripw)               
...........................
Difference-in-difference with Multiple Time Periods

                                                         Number of obs = 1,410
Outcome model  : least squares
Treatment model: inverse probability
------------------------------------------------------------------------------
             | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
g2034        |
 t_2031_2032 |  -254.8927   266.1024    -0.96   0.338    -776.4439    266.6584
 t_2032_2033 |  -257.5329   217.9389    -1.18   0.237    -684.6852    169.6194
 t_2033_2034 |   701.1318   127.0935     5.52   0.000     452.0331    950.2304
 t_2033_2035 |   1099.044   282.0704     3.90   0.000      546.196    1651.892
 t_2033_2036 |   1367.632   225.8702     6.05   0.000     924.9343    1810.329
 t_2033_2037 |   2008.294   237.2396     8.47   0.000     1543.313    2473.275
 t_2033_2038 |   2472.624   278.2949     8.88   0.000     1927.176    3018.072
 t_2033_2039 |   2689.615   504.3324     5.33   0.000     1701.142    3678.088
 t_2033_2040 |    3110.97    568.916     5.47   0.000     1995.915    4226.025
-------------+----------------------------------------------------------------
g2036        |
 t_2031_2032 |   216.0259   122.9107     1.76   0.079    -24.87472    456.9265
 t_2032_2033 |  -172.5154   372.0776    -0.46   0.643    -901.7741    556.7433
 t_2033_2034 |  -218.0495   504.5267    -0.43   0.666    -1206.904    770.8045
 t_2034_2035 |    621.033   156.1306     3.98   0.000     315.0227    927.0434
 t_2035_2036 |   999.0781   180.1055     5.55   0.000     646.0779    1352.078
 t_2035_2037 |   1003.333   250.5916     4.00   0.000     512.1829    1494.484
 t_2035_2038 |   1556.669   451.6914     3.45   0.001     671.3697    2441.967
 t_2035_2039 |   2590.674   662.6979     3.91   0.000      1291.81    3889.538
 t_2035_2040 |   2225.712   486.9917     4.57   0.000     1271.225    3180.198
-------------+----------------------------------------------------------------
g2037        |
 t_2031_2032 |   -121.857   169.1243    -0.72   0.471    -453.3345    209.6204
 t_2032_2033 |  -136.1117   193.9801    -0.70   0.483    -516.3057    244.0824
 t_2033_2034 |   35.53022   177.3557     0.20   0.841    -312.0805    383.1409
 t_2034_2035 |   138.6257   175.4021     0.79   0.429    -205.1561    482.4075
 t_2035_2036 |  -11.14846   177.0905    -0.06   0.950    -358.2394    335.9425
 t_2036_2037 |   1826.033    285.021     6.41   0.000     1267.402    2384.664
 t_2036_2038 |   2219.293   294.9304     7.52   0.000      1641.24    2797.346
 t_2036_2039 |   2630.665   284.4825     9.25   0.000      2073.09    3188.241
 t_2036_2040 |   3015.125   402.2712     7.50   0.000     2226.687    3803.562
------------------------------------------------------------------------------
Control: Never Treated

See Callaway and Sant'Anna (2021) for details

It looks to me that the gvar option for the csdid command act similarly to the cohortvar option fort the xthdidregress command. The gvar() option is used to specify the cohort variable.

[Jeff Wooldridge]

Hwanseong: It appears you have exit from treatment, potentially along with staggered entry. I know how this can be done using regression methods, but I don't believe xthdidregress or csdid support treatment patters with exit. Is the first treatment always in 2015 and the last always in 2020, or does that vary by firm?

[Hwanseong Pak]

Jeff Wooldridge
The first treatment and second always start at the same year(2015, 2018) for all firms.
I would appreciate it if you could explain or provide a link to the regression methods.
For now, I am using xthdidregress after removing the firms that exit the policy.
I am getting statisticall significant results with implications for the first group that was treated in 2015 but not for the group that was treated in 2018.
I am assuming this is because the group that was first treated in 2018 has a small sample size 80 compared to the 2015 group (1210) and never treated group (2238).
Could you please tell me if my current method and assumption are appropriate? If not, I will try the regression methods.

[Jeff Wooldridge]

I'm still not sure about the setup. It seems this is a staggered intervention, where some units are subjected to the treatment in 2015, and a different set is first treated in 2018. Is this correct? Are there two different treatments or two different intervention dates? Also, your simple example -- which you need to expand on -- shows exit from the treatment after 2020.