parallel trend test for staggered DiD

[Flora Yin]

Hello!

I'm conducting a parallel trend test for staggered DiD, this is the code I use

xtset firm year

gen distance = year - eventyear

replace distance = -3 if distance < -3
replace distance = 2 if distance > 2

forvalues i = -3(1)2 {
    gen `=strtoname("d`i'")' = (distance == `i')
}

drop d0

xtreg y d_3-d2 i.year controls ,fe vce(cluster firm)

The code has two parts, first create the relative year dummies, d_3 d_2 d_1 d0 d1 d2, the first 3 are 3 or more, 2, and 1 year(s) before the event year, and the last 3 are the event year and 1, 2 or more year(s) after the event year. Then I regress them with y, controls, and firm and year fixed effects.

What I'm confused about is that I have to drop a year (such as d0, or some other year) to be able to do the regression. Dropping different years will generate different results. If I put all the year dummies, one of them will be omitted.

if d0 is dropped
             |               Robust
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         d_3 |   .5068799    .498632     1.02   0.310    -.4719777    1.485738
         d_2 |    .152638   .2520139     0.61   0.545    -.3420871    .6473631
         d_1 |   .0003963   .1238065     0.00   0.997    -.2426466    .2434391
          d1 |  -.2798155   .1182116    -2.37   0.018     -.511875   -.0477559
          d2 |  -.3843642   .1621353    -2.37   0.018    -.7026497   -.0660787

if d_3 is dropped
                             Robust
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         d_2 |  -.3542419   .5307144    -0.67   0.505     -1.39608    .6875962
         d_1 |  -.5064837   .5103356    -0.99   0.321    -1.508316    .4953491
          d0 |  -.5068799    .498632    -1.02   0.310    -1.485738    .4719777
          d1 |  -.7866954   .5150054    -1.53   0.127    -1.797695    .2243047
          d2 |  -.8912441   .5520619    -1.61   0.107    -1.974989    .1925009
if put all 6 dummies in one regression
                             Robust
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         d_3 |   .8912441   .5520619     1.61   0.107    -.1925009    1.974989
         d_2 |   .5370022   .3235859     1.66   0.097    -.0982248    1.172229
         d_1 |   .3847605   .2219903     1.73   0.083    -.0510257    .8205467
          d0 |   .3843642   .1621353     2.37   0.018     .0660787    .7026497
          d1 |   .1045487   .1402132     0.75   0.456    -.1707018    .3797992
          d2 |          0  (omitted)

I find some papers regress all the year dummies in the same regression, so I suppose this is possible. How can I achieve something like this? Thanks!