Implementing Wooldridge DiD with more covariates

[Henry Strawforrd]

I am trying to understand the Jeff Wooldridge DiD estimation with more and binary covariates:

1. Do we also center binary X? Isn't a bit strange to have the effect then for a value that the X cannot take?
2. How many orders of interactions do we have to do as the number of covariates grows? For example, do we also have to take x1#x2#x3#d or just each covariate separately with x? And do we have to also interact all the covariates x1#x2#x3?

Below, I have modified the did_common_6 dataset to include two more time-invariant controls, one binary and one not.

* Example generated by -dataex-. For more info, type help dataex
clear
input int(id year) byte(f01 f02 f03 f04 f05 f06) float(x0 x1 c u) byte d float(y0 y1 y) byte w float(te x2 x3)
 1 2004 0 0 0 1 0 0   .3060876  .8999839 -1.3061992    -3.04351 0 16.500282 17.932508 16.500282 0  1.4322262 1  20.25588
 1 2005 0 0 0 0 1 0  1.6481395  .8999839 -1.3061992    .3134679 0  19.95726  23.33045  19.95726 0    3.37319 1  20.25588
 1 2003 0 0 1 0 0 0  .06370142  .8999839 -1.3061992   -.8482413 0 18.295551 18.295551 18.295551 0          0 1  20.25588
 1 2006 0 0 0 0 0 1  1.6340377  .8999839 -1.3061992   .12209804 0  19.86589  26.33341  19.86589 0    6.46752 1  20.25588
 1 2002 0 1 0 0 0 0  .58702457  .8999839 -1.3061992  -1.2422227 0  17.90157  17.90157  17.90157 0          0 1  20.25588
 1 2001 1 0 0 0 0 0  1.1609128  .8999839 -1.3061992   -.7842262 0 18.359566 18.359566 18.359566 0          0 1  20.25588
 2 2003 0 0 1 0 0 0  .19957064  .6742038  -.7233599  -1.6929256 0 17.920816 17.920816 17.920816 0          0 0 13.326492
 2 2004 0 0 0 1 0 0   .7170104  .6742038  -.7233599  -1.2869654 0 18.726776  21.47781 18.726776 0   2.751036 0 13.326492
 2 2001 1 0 0 0 0 0  .05028351  .6742038  -.7233599   -1.328019 0 18.285723 18.285723 18.285723 0          0 0 13.326492
 2 2002 0 1 0 0 0 0  1.2363397  .6742038  -.7233599   -.6061192 0 19.007624 19.007624 19.007624 0          0 0 13.326492
 2 2005 0 0 0 0 1 0  1.3075325  .6742038  -.7233599   .05444764 0  20.16819  27.04854  20.16819 0   6.880352 0 13.326492
 2 2006 0 0 0 0 0 1   .5344856  .6742038  -.7233599     3.03409 0  23.24783  26.72519  23.24783 0   3.477356 0 13.326492
 3 2006 0 0 0 0 0 1  .52091265  .7763655   .6008372    .4699862 0 22.059006   28.1483 22.059006 0   6.089294 1    7.5213
 3 2003 0 0 1 0 0 0   .4469955  .7763655   .6008372   1.8585327 0 22.847553 22.847553 22.847553 0          0 1    7.5213
 3 2005 0 0 0 0 1 0  .16134594  .7763655   .6008372    5.007066 0 26.496086 32.284145 26.496086 0   5.788059 1    7.5213
 3 2001 1 0 0 0 0 0    2.92056  .7763655   .6008372    .9024155 0 21.891436 21.891436 21.891436 0          0 1    7.5213
 3 2002 0 1 0 0 0 0  .58282447  .7763655   .6008372  -.11955032 0  20.86947  20.86947  20.86947 0          0 1    7.5213
 3 2004 0 0 0 1 0 0 .025554806  .7763655   .6008372  -2.1035151 0 19.285505  21.11419 19.285505 0   1.828684 1    7.5213
 4 2001 1 0 0 0 0 0  1.1238233  1.449669   .4445452   -2.695343 0 18.474037 18.474037 18.474037 0          0 0  24.36316
 4 2006 0 0 0 0 0 1  3.1662574  1.449669   .4445452   1.4399977 0  23.20938  31.30966  23.20938 0   8.100281 0  24.36316
 4 2002 0 1 0 0 0 0  .17738506  1.449669   .4445452   -2.460038 0 18.709341 18.709341 18.709341 0          0 0  24.36316
 4 2003 0 0 1 0 0 0  2.2930093  1.449669   .4445452   .10792396 0 21.277304 21.277304 21.277304 0          0 0  24.36316
 4 2005 0 0 0 0 1 0  1.7174016  1.449669   .4445452   .27073693 0 21.940117 26.899115 21.940117 0   4.958998 0  24.36316
 4 2004 0 0 0 1 0 0   .2201381  1.449669   .4445452   1.0744053 0 22.643785 27.047035 22.643785 0  4.4032497 0  24.36316
 5 2006 0 0 0 0 0 1  .06161892  1.481589   .0309765   1.0129526 0 22.384724 24.389465 22.384724 0  2.0047417 1 17.433357
 5 2001 1 0 0 0 0 0  .55583376  1.481589   .0309765   .01085913 0  20.78263  20.78263  20.78263 0          0 1 17.433357
 5 2004 0 0 0 1 0 0  1.2494304  1.481589   .0309765    3.886539 0  25.05831   30.0035  25.05831 0    4.94519 1 17.433357
 5 2002 0 1 0 0 0 0  .12433722  1.481589   .0309765    .3325454 0 21.104317 21.104317 21.104317 0          0 1 17.433357
 5 2003 0 0 1 0 0 0  .33023635  1.481589   .0309765    3.059907 0  23.83168  23.83168  23.83168 0          0 1 17.433357
 5 2005 0 0 0 0 1 0   6.568078  1.481589   .0309765    1.451638 0  22.72341  25.80217  22.72341 0   3.078762 1 17.433357
 6 2002 0 1 0 0 0 0  .15857266  .4216814 -1.5163058   1.9113857 0  20.60592  20.60592  20.60592 0          0 0  6.055562
 6 2003 0 0 1 0 0 0   .4737925  .4216814 -1.5163058     .372273 0 19.066809 19.066809 19.066809 0          0 0  6.055562
 6 2001 1 0 0 0 0 0   .6631577  .4216814 -1.5163058  -2.0006878 0 16.693848 16.693848 16.693848 0          0 0  6.055562
 6 2005 0 0 0 0 1 0   .8055798  .4216814 -1.5163058    3.693907 0  22.88844  29.61216  22.88844 0   6.723721 0  6.055562
 6 2004 0 0 0 1 0 0  .09303146  .4216814 -1.5163058   -2.445572 0 16.648962  19.23068 16.648962 0    2.58172 0  6.055562
 6 2006 0 0 0 0 0 1  .33595455  .4216814 -1.5163058  -1.6402093 0 17.654325 24.942156 17.654325 0    7.28783 0  6.055562
 7 2003 0 0 1 0 0 0   2.819954 2.2678227   .7179165   4.1437035 1  23.99553  23.99553  23.99553 0          0 1 10.237764
 7 2001 1 0 0 0 0 0  .37007815 2.2678227   .7179165    .3543251 1 20.206154 20.206154 20.206154 0          0 1 10.237764
 7 2005 0 0 0 0 1 0   1.451097 2.2678227   .7179165  -.18847714 1  20.16335   24.9257   24.9257 1  4.7623463 1 10.237764
 7 2002 0 1 0 0 0 0   3.602984 2.2678227   .7179165   -3.009033 1 16.842794 16.842794 16.842794 0          0 1 10.237764
 7 2004 0 0 0 1 0 0   .9396546 2.2678227   .7179165     2.77177 1   23.0236  28.11396  28.11396 1   5.090361 1 10.237764
 7 2006 0 0 0 0 0 1   4.423169 2.2678227   .7179165   4.6137824 1  25.06561 30.886784 30.886784 1   5.821173 1 10.237764
 8 2006 0 0 0 0 0 1   2.153845   1.35818   1.555748  -.08226311 0 22.752575 28.737257 22.752575 0   5.984682 0  3.103299
 8 2005 0 0 0 0 1 0   .4518185   1.35818   1.555748   -.7949974 0  21.93984 27.426264  21.93984 0   5.486423 0  3.103299
 8 2004 0 0 0 1 0 0  1.9123118   1.35818   1.555748    .9501973 0 23.585035  23.50792 23.585035 0 -.07711792 0  3.103299
 8 2002 0 1 0 0 0 0   1.718524   1.35818   1.555748   -3.419948 0  18.81489  18.81489  18.81489 0          0 0  3.103299
 8 2001 1 0 0 0 0 0   .6112706   1.35818   1.555748  -.18530323 0 22.049534 22.049534 22.049534 0          0 0  3.103299
 8 2003 0 0 1 0 0 0  1.3013097   1.35818   1.555748  -1.2717605 0  20.96308  20.96308  20.96308 0          0 0  3.103299
 9 2004 0 0 0 1 0 0  .24888325 1.2267038 -1.8302025    -2.40967 1  14.77348 18.539341 18.539341 1  3.7658615 1  7.103189
 9 2001 1 0 0 0 0 0   .8760293 1.2267038 -1.8302025    3.524959 1  20.30811  20.30811  20.30811 0          0 1  7.103189
 9 2003 0 0 1 0 0 0   .9204704 1.2267038 -1.8302025    .8833148 1 17.666464 17.666464 17.666464 0          0 1  7.103189
 9 2006 0 0 0 0 0 1   5.113919 1.2267038 -1.8302025    3.549654 1 20.932804  26.25754  26.25754 1   5.324738 1  7.103189
 9 2002 0 1 0 0 0 0  .13916393 1.2267038 -1.8302025   -.9547358 1 15.828414 15.828414 15.828414 0          0 1  7.103189
 9 2005 0 0 0 0 1 0  .06175615 1.2267038 -1.8302025   1.7848247 1 19.067974  25.55248  25.55248 1   6.484509 1  7.103189
10 2002 0 1 0 0 0 0  .43844765  .4105914 -1.5521548  -2.1601157 1 14.493025 14.493025 14.493025 0          0 0 17.930876
10 2005 0 0 0 0 1 0   .8831286  .4105914 -1.5521548   -.7734712 1  16.37967 19.114056 19.114056 1  2.7343864 0 17.930876
10 2004 0 0 0 1 0 0    .413378  .4105914 -1.5521548    .5969602 1   17.6501 20.411837 20.411837 1   2.761736 0 17.930876
10 2006 0 0 0 0 0 1  .14171585  .4105914 -1.5521548    2.750983 1 20.004124  25.92111  25.92111 1   5.916985 0 17.930876
10 2003 0 0 1 0 0 0  .06419521  .4105914 -1.5521548    .4602623 1 17.113403 17.113403 17.113403 0          0 0 17.930876
10 2001 1 0 0 0 0 0   .5226828  .4105914 -1.5521548  -.05229951 1 16.600842 16.600842 16.600842 0          0 0 17.930876
11 2001 1 0 0 0 0 0   .6422579  .9265445 -4.3990397   -.4590163 1 13.605216 13.605216 13.605216 0          0 1 10.327092
11 2003 0 0 1 0 0 0   .5846129  .9265445 -4.3990397   2.3547597 1 16.418993 16.418993 16.418993 0          0 1 10.327092
11 2004 0 0 0 1 0 0  2.1288738  .9265445 -4.3990397   -1.239237 1 13.224996 13.350397 13.350397 1   .1254015 1 10.327092
11 2006 0 0 0 0 0 1  1.0985651  .9265445 -4.3990397    1.735612 1 16.399845  23.97114  23.97114 1   7.571297 1 10.327092
11 2002 0 1 0 0 0 0  .17319475  .9265445 -4.3990397  -.17446163 1  13.88977  13.88977  13.88977 0          0 1 10.327092
11 2005 0 0 0 0 1 0   .9317628  .9265445 -4.3990397  -1.6626803 1 12.901552 18.886393 18.886393 1    5.98484 1 10.327092
12 2005 0 0 0 0 1 0   .7289661  .8532412 -1.7565117   1.2556676 0  20.42578 24.444366  20.42578 0   4.018589 0   7.90556
12 2006 0 0 0 0 0 1   .6080928  .8532412 -1.7565117   -2.910625 0 16.359484 23.278046 16.359484 0   6.918562 0   7.90556
12 2001 1 0 0 0 0 0   2.067974  .8532412 -1.7565117   1.5269603 0  20.19707  20.19707  20.19707 0          0 0   7.90556
12 2004 0 0 0 1 0 0   .6054283  .8532412 -1.7565117  -1.9526075 0 17.117502 19.585154 17.117502 0  2.4676514 0   7.90556
12 2002 0 1 0 0 0 0  .04738205  .8532412 -1.7565117  -2.8624616 0 15.807648 15.807648 15.807648 0          0 0   7.90556
12 2003 0 0 1 0 0 0  1.0616038  .8532412 -1.7565117   -2.705209 0   15.9649   15.9649   15.9649 0          0 0   7.90556
13 2003 0 0 1 0 0 0  .22429258 1.0197799  -5.042834  -.49931705 0  14.96774  14.96774  14.96774 0          0 1 12.138537
13 2006 0 0 0 0 0 1  1.1751271 1.0197799  -5.042834   -2.968002 0 13.099053  19.35392 13.099053 0   6.254867 1 12.138537
13 2005 0 0 0 0 1 0   .7750041 1.0197799  -5.042834    .9949038 0  16.96196 18.287554  16.96196 0   1.325594 1 12.138537
13 2004 0 0 0 1 0 0   .4676123 1.0197799  -5.042834   2.1828074 0 18.049864    19.508 18.049864 0  1.4581356 1 12.138537
13 2002 0 1 0 0 0 0  2.0277784 1.0197799  -5.042834  -1.0009137 0 14.466142 14.466142 14.466142 0          0 1 12.138537
13 2001 1 0 0 0 0 0  1.4488647 1.0197799  -5.042834  -.16259946 0 15.304456 15.304456 15.304456 0          0 1 12.138537
14 2005 0 0 0 0 1 0  .28565294  .8468386  .17828622   2.0193295 1 21.121035  27.22845  27.22845 1   6.107416 0  4.854001
14 2004 0 0 0 1 0 0   .9807044  .8468386  .17828622   -1.837703 1 17.164003 23.513033 23.513033 1    6.34903 0  4.854001
14 2003 0 0 1 0 0 0  1.1919093  .8468386  .17828622 -.017519366 1 18.584187 18.584187 18.584187 0          0 0  4.854001
14 2002 0 1 0 0 0 0   .9409264  .8468386  .17828622  .023804275 1  18.62551  18.62551  18.62551 0          0 0  4.854001
14 2006 0 0 0 0 0 1   .4886237  .8468386  .17828622  -1.0913773 1 18.110329 22.842997 22.842997 1   4.732668 0  4.854001
14 2001 1 0 0 0 0 0  1.1932147  .8468386  .17828622   -1.229629 1 17.372076 17.372076 17.372076 0          0 0  4.854001
15 2003 0 0 1 0 0 0   .7850884 1.2177105  2.8261676   -2.441496 0 20.993526 20.993526 20.993526 0          0 1 17.053638
15 2002 0 1 0 0 0 0  .22712035 1.2177105  2.8261676  -.23791227 0  23.19711  23.19711  23.19711 0          0 1 17.053638
15 2005 0 0 0 0 1 0  2.1530826 1.2177105  2.8261676   .24793527 0  24.18296  27.45808  24.18296 0   3.275122 1 17.053638
15 2001 1 0 0 0 0 0  .42704725 1.2177105  2.8261676   1.3548107 0 24.789833 24.789833 24.789833 0          0 1 17.053638
15 2006 0 0 0 0 0 1  1.1538873 1.2177105  2.8261676  -2.4069495 0  21.62807  26.95773  21.62807 0   5.329655 1 17.053638
15 2004 0 0 0 1 0 0  2.5600374 1.2177105  2.8261676   -1.515538 0 22.319485 26.113136 22.319485 0  3.7936516 1 17.053638
16 2002 0 1 0 0 0 0   1.649291  .8262194  -3.039424   -.4664764 1  14.90721  14.90721  14.90721 0          0 0  3.632325
16 2006 0 0 0 0 0 1   .9343096  .8262194  -3.039424  -1.0802279 1 14.893457 20.608376 20.608376 1   5.714918 0  3.632325
16 2001 1 0 0 0 0 0   .4561211  .8262194  -3.039424   -1.511918 1 13.861768 13.861768 13.861768 0          0 0  3.632325
16 2003 0 0 1 0 0 0   1.208848  .8262194  -3.039424  -2.5091746 1  12.86451  12.86451  12.86451 0          0 0  3.632325
16 2005 0 0 0 0 1 0  .12327927  .8262194  -3.039424   1.5102085 1 17.383894  24.67079  24.67079 1   7.286896 0  3.632325
16 2004 0 0 0 1 0 0   .5854673  .8262194  -3.039424    .3695994 1 16.143286  19.57702  19.57702 1   3.433737 0  3.632325
17 2002 0 1 0 0 0 0   1.905228 .54959255  1.8770715  -1.1472305 0 21.004637 21.004637 21.004637 0          0 1  20.80849
17 2006 0 0 0 0 0 1   .3304343 .54959255  1.8770715  -1.8845243 0 20.867344 25.007227 20.867344 0   4.139883 1  20.80849
17 2003 0 0 1 0 0 0   .2024587 .54959255  1.8770715  -1.2083232 0 20.943544 20.943544 20.943544 0          0 1  20.80849
17 2001 1 0 0 0 0 0  .22234537 .54959255  1.8770715   1.6832645 0  23.83513  23.83513  23.83513 0          0 1  20.80849
end

Here is a try at extending the example to three covariates

sum x1 if d
gen x1_dm = x1 - r(mean)

sum x2 if d
gen x2_dm = x2 - r(mean)

sum x3 if d
gen x3_dm = x3 - r(mean)


reg y c.d#c.f04 c.d#c.f05 c.d#c.f06 c.year d x1_dm x2_dm x3_dm ///
    c.d#c.f04#c.x1_dm c.d#c.f05#c.x1_dm c.d#c.f06#c.x1_dm c.year#c.x1_dm c.d#c.x1_dm ///
    c.d#c.f04#c.x2_dm c.d#c.f05#c.x2_dm c.d#c.f06#c.x2_dm c.year#c.x2_dm c.d#c.x2_dm ///    
    c.d#c.f04#c.x3_dm c.d#c.f05#c.x3_dm c.d#c.f06#c.x3_dm c.year#c.x3_dm c.d#c.x3_dm ///
    c.d#c.f04#c.x1_dm#c.x2_dm c.d#c.f05#c.x1_dm#c.x2_dm c.d#c.f06#c.x1_dm#c.x2_dm c.year#c.x1_dm#c.x2_dm c.d#c.x1_dm#c.x2_dm ///
    c.d#c.f04#c.x1_dm#c.x3_dm c.d#c.f05#c.x1_dm#c.x3_dm c.d#c.f06#c.x1_dm#c.x3_dm c.year#c.x1_dm#c.x3_dm c.d#c.x1_dm#c.x3_dm ///
    c.d#c.f04#c.x2_dm#c.x3_dm c.d#c.f05#c.x2_dm#c.x3_dm c.d#c.f06#c.x2_dm#c.x3_dm c.year#c.x2_dm#c.x3_dm c.d#c.x2_dm#c.x3_dm ///
    c.d#c.f04#c.x1_dm#c.x2_dm#c.x3_dm c.d#c.f05#c.x1_dm#c.x2_dm#c.x3_dm c.d#c.f06#c.x1_dm#c.x2_dm#c.x3_dm ///
    c.year#c.x1_dm#c.x2_dm#c.x3_dm c.d#c.x1_dm#c.x2_dm#c.x3_dm ///
    c.x1_dm#c.x2_dm c.x2_dm#c.x3_dm c.x1_dm#c.x3_dm c.x1_dm#c.x2_dm#c.x3_dm ///
    , vce(cluster id)

However, the results are way off from what we got with only 1 covariate so I am thinking maybe it is too much?

[FernandoRios]

Hi Henry
Short answers.
1. Yes, you also need to estimate the mean of dummies.
2. You may want to check -jwdid- from ssc. It does all the averaging and calculations for you (assuming groups and periods are well defined)
Best wishes

[Henry Strawforrd]

Hi Fernando,

since it's a regression, I would prefer to be able to set it up myself as this would give me more flexibility.

Anyway, I tested jwdid on the dataset using one control like this (not quite sure if I should use d as gvar instead?)

jwdid y x1, ivar(id) tvar(year) gvar(w)

and it's giving me very strange output

[FernandoRios]

Agreed
Better to implement it by hand.
And it seems to me your W is not correctly defined. But cannot see why based on your output
Typical FAQ. What do you get if you tab year and gvar ?
F

[Henry Strawforrd]

Yes, indeed if I may give a small feedback: It's not entirely clear to me after reading the helpfile how gvar should be specified for jwdid.

w = D * Post, it is equal to one for the treated after 2003 in this example



. tab year w

| w
year | 0 1 | Total
-----------+----------------------+----------
2001 | 17 0 | 17
2002 | 17 0 | 17
2003 | 17 0 | 17
2004 | 10 6 | 16
2005 | 10 6 | 16
2006 | 11 6 | 17
-----------+----------------------+----------
Total | 82 18 | 100

[FernandoRios]

Got it
gvar is the year where a unit is treated.
so whenever treatxpost is one for the first time, that is the cohort for that observation
in any case, I ll be updating jwdid to allow use of gvar or treatment
email me for an early release
fernando

[Henry Strawforrd]

Great!

So, what regression would jwdid run if we have repeated cross-sections?

[Henry Strawforrd]

Does this center the covariates around the treated mean? Not completely sure to me the code would do that

** Center Covariates
    if "`weight'"!="" local wgt aw
    if "`x'"!="" {
            capture drop _x_*
            qui:hdfe `y' `x' if `touse'    [`wgt'`exp'], abs(`gvar')     keepsingletons  gen(_x_)
            capture drop _x_`y'
            local xxvar _x_*
    }
    ***

[Henry Strawforrd]

And what is this doing?

local xvar `xvar' c.__tr__#i`i'.`gvar'#i`j'.`tvar' ///
c.__tr__#i`i'.`gvar'#i`j'.`tvar'#c.(`xxvar')

[FernandoRios]

Yes it will still run if you have repeated crossection
check here for some examples
https://friosavila.github.io/app_met..._metrics8.html

the code you point out does create the variables demeaning around cohort means

and The last set of codes simply selects what to include in the regression

[Jeff Wooldridge]

The reason you got strange answers with lots of interactions among the controls is because you'd need to demean the interactions themselves to obtain the ATTs. That's why it's easiest to use w (time-varying treatment) in place of d in the interactions with the time dummies and then obtain the average marginal effects with respect to w (averaged across the cohort-time pair). Demeaning each x does not mean that x1_dm#x2_dm has mean zero; it generally does not.

[Julie Martin]

Dear all, I am trying to do a triple diff-in-diff using Wooldrige (2021) approach, and I am not sure how to do that. After jwdid (or the equivalent regression) with a binary covariate x, should we evaluate margins at w=1 and- (i) x =( 0 1) or at (ii) x_dm = (min max) or at (iii) x_dm = (0 1)?

What I am doing is (ii). After jwdid I use "margins , subpop(if __etr__==1) at(__tr__=(0 1) _x_woman= ( -0.58 0.41)) noestimcheck contrast(atcontrast(r)) post

Many thanks!

[FernandoRios]

Hi Julie
For DDD, JWDID will not do the work, because it assumes DD only.
What i think would need to be modified is to modify the specification and interact all current interactions by the Female dummy. I think that will work if no covariates are included, but not so sure if you add covariates (at least not without further data manipulation)
HTH
Fernando

[Julie Martin]

thank you!!

[Jeff Wooldridge]

It does become DDD if you specify the only covariate to be "female" and then look at the moderating (interaction) effects that look like dg*fs*female that are reported by jwdid. That's one of many reasons I like this command because you see those effects. Equivalently, run jwdid twice, once with female = 0 and once with female = 1, and then take the difference of the estimated effects. (These will be numerically the same as including female as the only covariate).

I came to realize awhile back that this is yet another advantage of the regression-based approach. One can do DDD using another control group or DDD across time (by including heterogeneous trends).

To allow time-constant covariates to do DDD in jwdid, you'd have to demean those covariates by hand using the female means, and then include them along with female in the list of covariates. I should admit that this is a bit of conjecturing, so I'll work it out. Something that will definitely work is to do the estimation separately for female = 0 and female = 1, including the controls x. Then difference the results as above. The problem would be in getting a standard error using jwdid.