I have problem with re-producing results using the same data using reghdfe command.

The version of Stata I am using is Stata/MP 14.2. I am on Windows 10.

There are two methods below:
The first regression uses i.time;
the second method creates individual dummy variables for each value of "time" manually, and then regress y on these individual dummy variables.

I think the two are supposed to produce the same results, however, the sign of the coefficients flip, while other stats remain the same.

It seems that a similar question is posted here: https://www.statalist.org/forums/for...-effects-model
But it doesn't seem that the problem has been resolved, and I am not using standardization.

This is an example:

Data generating:
Code:
* generating example:
clear all
set obs 60
set seed 10101
gen id =_n

expand 11
drop in 1/60
count

bys id: gen time = _n+1999
xtset id time

gen x1 = rnormal(1,7)
gen x2 = rnormal(2,5)

sort time id
by time: gen ind = _n
sort id time
by id: gen T = _n

gen D = 0 
replace D = 1 if  id > 29
gen post = 0
replace post = 1 if time >= 2005

bysort id: gen y0 = 10  + 5 * x1 + 3 * x2 + T + ind + rnormal()
bysort id: gen y1 = 10  + 5 * x1 + 3 * x2 + T + ind + rnormal() if time < 2005
bysort id: replace y1 = 10  + 5 * x1 + 3 * x2 + T*5 + ind + rnormal() if time >= 2005

gen y = y0 + D * (y1 - y0)

First regression and output:
Code:
* first way of using reghdfe
reghdfe y i.D#i.time x1 x2, vce(robust) absorb(id time)

* results:
. reghdfe y i.D#i.time x1 x2, vce(robust) absorb(id time)
(MWFE estimator converged in 2 iterations)
note: 1.D#2000b.time omitted because of collinearity
note: 1.D#2001.time omitted because of collinearity
note: 1.D#2002.time omitted because of collinearity
note: 1.D#2003.time omitted because of collinearity
note: 1.D#2004.time omitted because of collinearity
note: 1.D#2005.time omitted because of collinearity
note: 1.D#2006.time omitted because of collinearity
note: 1.D#2007.time omitted because of collinearity
note: 1.D#2008.time omitted because of collinearity
note: 1.D#2009.time omitted because of collinearity

HDFE Linear regression                            Number of obs   =        600
Absorbing 2 HDFE groups                           F(  11,    520) =   73420.88
                                                  Prob > F        =     0.0000
                                                  R-squared       =     0.9996
                                                  Adj R-squared   =     0.9996
                                                  Within R-sq.    =     0.9993
                                                  Root MSE        =     1.0198

------------------------------------------------------------------------------
             |               Robust
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      D#time |
     0 2001  |  -.4300092   .3876248    -1.11   0.268    -1.191512    .3314938
     0 2002  |  -.5771689   .4019524    -1.44   0.152    -1.366819    .2124813
     0 2003  |   -.429583   .3970868    -1.08   0.280    -1.209674    .3505086
     0 2004  |  -.0252408   .4055941    -0.06   0.950    -.8220453    .7715637
     0 2005  |  -23.81867   .3902227   -61.04   0.000    -24.58527   -23.05206
     0 2006  |   -28.3694   .3752589   -75.60   0.000    -29.10661   -27.63219
     0 2007  |  -32.00615   .3955035   -80.93   0.000    -32.78314   -31.22917
     0 2008  |  -36.16594    .411139   -87.97   0.000    -36.97363   -35.35824
     0 2009  |  -40.40244   .4017046  -100.58   0.000    -41.19161   -39.61328
     1 2000  |          0  (omitted)
     1 2001  |          0  (omitted)
     1 2002  |          0  (omitted)
     1 2003  |          0  (omitted)
     1 2004  |          0  (omitted)
     1 2005  |          0  (omitted)
     1 2006  |          0  (omitted)
     1 2007  |          0  (omitted)
     1 2008  |          0  (omitted)
     1 2009  |          0  (omitted)
             |
          x1 |   4.998795   .0061697   810.22   0.000     4.986675    5.010916
          x2 |   3.002194   .0087326   343.79   0.000     2.985039     3.01935
       _cons |   62.15612   .1440129   431.60   0.000      61.8732    62.43904
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
          id |        60           0          60     |
        time |        10           1           9     |
-----------------------------------------------------+

Second regression and output:
Code:
* second way of doing the same thing"

. 
. tab time, gen(year)

       time |      Freq.     Percent        Cum.
------------+-----------------------------------
       2000 |         60       10.00       10.00
       2001 |         60       10.00       20.00
       2002 |         60       10.00       30.00
       2003 |         60       10.00       40.00
       2004 |         60       10.00       50.00
       2005 |         60       10.00       60.00
       2006 |         60       10.00       70.00
       2007 |         60       10.00       80.00
       2008 |         60       10.00       90.00
       2009 |         60       10.00      100.00
------------+-----------------------------------
      Total |        600      100.00



. reghdfe y c.D#(c.year2-year10) x1 x2, absorb(id time) vce(robust)
(MWFE estimator converged in 2 iterations)

HDFE Linear regression                            Number of obs   =        600
Absorbing 2 HDFE groups                           F(  11,    520) =   73420.88
                                                  Prob > F        =     0.0000
                                                  R-squared       =     0.9996
                                                  Adj R-squared   =     0.9996
                                                  Within R-sq.    =     0.9993
                                                  Root MSE        =     1.0198

------------------------------------------------------------------------------
             |               Robust
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
 c.D#c.year2 |   .4300092   .3876248     1.11   0.268    -.3314938    1.191512
             |
 c.D#c.year3 |   .5771689   .4019524     1.44   0.152    -.2124813    1.366819
             |
 c.D#c.year4 |    .429583   .3970868     1.08   0.280    -.3505086    1.209674
             |
 c.D#c.year5 |   .0252408   .4055941     0.06   0.950    -.7715637    .8220453
             |
 c.D#c.year6 |   23.81867   .3902227    61.04   0.000     23.05206    24.58527
             |
 c.D#c.year7 |    28.3694   .3752589    75.60   0.000     27.63219    29.10661
             |
 c.D#c.year8 |   32.00615   .3955035    80.93   0.000     31.22917    32.78314
             |
 c.D#c.year9 |   36.16594    .411139    87.97   0.000     35.35824    36.97363
             |
c.D#c.year10 |   40.40244   .4017046   100.58   0.000     39.61328    41.19161
             |
          x1 |   4.998795   .0061697   810.22   0.000     4.986675    5.010916
          x2 |   3.002194   .0087326   343.79   0.000     2.985039     3.01935
       _cons |   45.93366   .1506753   304.85   0.000     45.63765    46.22967
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
          id |        60           0          60     |
        time |        10           1           9     |
-----------------------------------------------------+
Does anybody know why this is the case?

Thank you!