Hello everyone,

I am presenting an interesting problem here, at least interesting and at the same time weird to me. I am running an OLS regression using reg command. I have three continuous variables and one binary treatment variable. In addition, I want to include year fixed effects, district fixed effects, and unit fixed effects using the factor variable notation in Stata (i.varname). However, my coefficients are sensitive to the ordering of factor variables. For example when I run:

Code:
global xlist classsize teacher_perstudent higheduc_teacher_perstudent i.districteng i.schoolid i.progyear 
reg avgscore_male_nonretaker t $xlist, cluster(schoolid) allbaselevels
I am getting this

PHP Code:
Linear regression                               Number of obs     =         43
                                                F
(529)          =          .
                                                
Prob F          =          .
                                                
R-squared         =     0.9698
                                                Root MSE          
=      12.95

                                             
(StdErradjusted for 30 clusters in schoolid)
---------------------------------------------------------------------------------------------
                            |               
Robust
   avgscore_male_nonretaker 
|      Coef.   StdErr.      t    P>|t|     [95ConfInterval]
----------------------------+----------------------------------------------------------------
                          
|   18.75526   42.49063     0.44   0.662    -68.14784    105.6583
                  classsize 
|  -.1132929   1.046558    -0.11   0.915    -2.253744    2.027158
         teacher_perstudent 
|   16.13461   19.98505     0.81   0.426    -24.73941    57.00864
higheduc_teacher_perstudent 
|  -28.82376    58.8787    -0.49   0.628    -149.2442    91.59671
                            
|
                
districteng |
                
Dai Mirdad  |          0  (base)
           
Dara i Suf Bala  |   122.3196   33.65303     3.63   0.001     53.49143    191.1478
                     Gizab  
|   49.01942   101.9663     0.48   0.634     -159.525    257.5639
                   Jalreez  
|   104.6114   438.0338     0.24   0.813    -791.2684    1000.491
              Khas Uruzgan  
|   71.54592   58.80817     1.22   0.234     -48.7303    191.8221
                      Kiti  
|   48.78746   22.03812     2.21   0.035     3.714444    93.86049
          Lal o Sar Jangal  
|  -26.31099   107.3473    -0.25   0.808    -245.8608    193.2388
                  Malistan  
|   88.19973   46.43968     1.90   0.068    -6.780067    183.1795
             Markaz Behsud  
|   1.466345    54.6986     0.03   0.979    -110.4049    113.3375
                  Miramoor  
|   50.78536   61.51352     0.83   0.416    -75.02392    176.5946
                     Nahor  
|   92.51837     29.796     3.11   0.004     31.57871     153.458
                    Panjab  
|   21.75951   26.68676     0.82   0.422    -32.82105    76.34007
                 Roy 
do Ab  |   54.42585   42.86992     1.27   0.214    -33.25297    142.1047
                Shahristan  
|   63.03825   19.94752     3.16   0.004     22.24099    103.8355
                 Shikh Ali  
|  -22.67487   49.27363    -0.46   0.649    -123.4508    78.10102
                     Waras  
|   60.66022   30.47429     1.99   0.056     -1.66669    122.9871
                 Yakawlang  
|    42.0939   31.28532     1.35   0.189    -21.89176    106.0796
                            
|
                   
progyear |
                      
2014  |          0  (base)
                      
2015  |  -37.10014   47.96113    -0.77   0.445    -135.1917    60.99138
                      2016  
|  -51.78048   97.60409    -0.53   0.600    -251.4033    147.8423
                      2017  
|  -83.51801   140.8801    -0.59   0.558    -371.6502    204.6142
                            
|
                   
schoolid |
                 
150300010  |          0  (base)
                 
150300019  |  -58.26665   97.24575    -0.60   0.554    -257.1565    140.6232
                 150300026  
|  -78.04578   53.70461    -1.45   0.157     -187.884    31.79248
                 150500016  
|          0  (omitted)
                 
260300005  |          0  (omitted)
                 
260400001  |  -11.29118   39.35719    -0.29   0.776    -91.78568    69.20332
                 260400002  
|          0  (omitted)
                 
270700022  |   122.8894   103.3797     1.19   0.244    -88.54591    334.3247
                 270700048  
|          0  (omitted)
                 
280400012  |  -55.59268   40.07616    -1.39   0.176    -137.5576    26.37227
                 280400018  
|          0  (omitted)
                 
280500003  |   18.90369   49.73354     0.38   0.707    -82.81283    120.6202
                 280500036  
|          0  (omitted)
                 
280600047  |          0  (omitted)
                 
306000018  |          0  (omitted)
                 
340600022  |          0  (omitted)
                 
340700013  |  -32.15847    66.5693    -0.48   0.633     -168.308     103.991
                 340700028  
|          0  (omitted)
                 
340900024  |          0  (omitted)
                 
402000012  |  -97.33107   421.7379    -0.23   0.819     -959.882    765.2199
                 402000019  
|          0  (omitted)
                 
404000010  |   53.02595   32.69272     1.62   0.116    -13.83818    119.8901
                 404000033  
|  -39.52184   47.86309    -0.83   0.416    -137.4128    58.36917
                 404000035  
|  -85.81084   72.24248    -1.19   0.245    -233.5633    61.94163
                 404000043  
|   24.28322   102.5233     0.24   0.814    -185.4005    233.9669
                 404000073  
|          0  (omitted)
                 
405000008  |          0  (omitted)
                 
604000098  |          0  (omitted)
                 
604000103  |          0  (omitted)
                 
606000070  |          0  (omitted)
                            |
                      
_cons |   167.3151   45.65664     3.66   0.001     73.93678    260.6934
--------------------------------------------------------------------------------------------- 
But when I change the order of just two factor variables as follows:

Code:
global xlist classsize teacher_perstudent higheduc_teacher_perstudent i.districteng i.schoolid i.progyear 
reg avgscore_male_nonretaker t $xlist, cluster(schoolid) allbaselevels
I am getting the following result:

PHP Code:
Linear regression                               Number of obs     =         43
                                                F
(529)          =          .
                                                
Prob F          =          .
                                                
R-squared         =     0.9698
                                                Root MSE          
=      12.95

                                             
(StdErradjusted for 30 clusters in schoolid)
---------------------------------------------------------------------------------------------
                            |               
Robust
   avgscore_male_nonretaker 
|      Coef.   StdErr.      t    P>|t|     [95ConfInterval]
----------------------------+----------------------------------------------------------------
                          
|   -9.08408   12.34954    -0.74   0.468    -34.34173    16.17356
                  classsize 
|  -.1132929   1.046558    -0.11   0.915    -2.253744    2.027158
         teacher_perstudent 
|   16.13461   19.98505     0.81   0.426    -24.73941    57.00864
higheduc_teacher_perstudent 
|  -28.82376    58.8787    -0.49   0.628    -149.2442    91.59671
                            
|
                
districteng |
                
Dai Mirdad  |          0  (base)
           
Dara i Suf Bala  |   94.48027    32.3545     2.92   0.007     28.30789    160.6527
                     Gizab  
|   104.6981   18.04242     5.80   0.000     67.79721     141.599
                   Jalreez  
|   48.93273   516.7161     0.09   0.925     -1007.87    1105.736
              Khas Uruzgan  
|   99.38525   31.14976     3.19   0.003     35.67684    163.0937
                      Kiti  
|   48.78746   22.03812     2.21   0.035     3.714444    93.86049
          Lal o Sar Jangal  
|   29.36768   21.85836     1.34   0.190     -15.3377    74.07305
                  Malistan  
|   88.19973   46.43968     1.90   0.068    -6.780067    183.1795
             Markaz Behsud  
|   29.30568   13.08261     2.24   0.033     2.548731    56.06263
                  Miramoor  
|    78.6247   18.00107     4.37   0.000     41.80838     115.441
                     Nahor  
|   92.51837     29.796     3.11   0.004     31.57871     153.458
                    Panjab  
|   21.75951   26.68676     0.82   0.422    -32.82105    76.34007
                 Roy 
do Ab  |   54.42585   42.86992     1.27   0.214    -33.25297    142.1047
                Shahristan  
|   63.03825   19.94752     3.16   0.004     22.24099    103.8355
                 Shikh Ali  
|  -22.67487   49.27363    -0.46   0.649    -123.4508    78.10102
                     Waras  
|   32.82089   74.72315     0.44   0.664    -120.0051    185.6469
                 Yakawlang  
|    42.0939   31.28532     1.35   0.189    -21.89176    106.0796
                            
|
                   
schoolid |
                 
150300010  |          0  (base)
                 
150300019  |  -2.587977   9.719837    -0.27   0.792    -22.46727    17.29132
                 150300026  
|  -50.20644   16.52537    -3.04   0.005    -84.00462   -16.40826
                 150500016  
|          0  (omitted)
                 
260300005  |          0  (omitted)
                 
260400001  |  -39.13052   12.62379    -3.10   0.004    -64.94907   -13.31196
                 260400002  
|          0  (omitted)
                 
270700022  |   39.37137   49.03798     0.80   0.429    -60.92255    139.6653
                 270700048  
|          0  (omitted)
                 
280400012  |  -27.75334   25.84329    -1.07   0.292     -80.6088    25.10212
                 280400018  
|          0  (omitted)
                 
280500003  |  -8.935647    20.8451    -0.43   0.671    -51.56866    33.69736
                 280500036  
|          0  (omitted)
                 
280600047  |          0  (omitted)
                 
306000018  |          0  (omitted)
                 
340600022  |          0  (omitted)
                 
340700013  |  -59.99781    28.1416    -2.13   0.042    -117.5538   -2.441779
                 340700028  
|          0  (omitted)
                 
340900024  |          0  (omitted)
                 
402000012  |   -41.6524   500.2204    -0.08   0.934    -1064.718    981.4132
                 402000019  
|          0  (omitted)
                 
404000010  |   25.18661   32.97342     0.76   0.451     -42.2516    92.62483
                 404000033  
|   -11.6825   25.76335    -0.45   0.654    -64.37447    41.00947
                 404000035  
|  -57.97151   64.91141    -0.89   0.379    -190.7302    74.78724
                 404000043  
|  -59.23479   55.16953    -1.07   0.292    -172.0692    53.59958
                 404000073  
|          0  (omitted)
                 
405000008  |          0  (omitted)
                 
604000098  |  -27.83934   46.96004    -0.59   0.558    -123.8834    68.20473
                 604000103  
|          0  (omitted)
                 
606000070  |          0  (omitted)
                            |
                   
progyear |
                      
2014  |          0  (base)
                      
2015  |  -9.260804   14.20829    -0.65   0.520    -38.32003    19.79842
                      2016  
|   3.898195   16.14454     0.24   0.811    -29.12109    36.91748
                      2017  
|          0  (omitted)
                            |
                      
_cons |   139.4757   43.84943     3.18   0.003     49.79359    229.1579
--------------------------------------------------------------------------------------------- 

Please take a look at the coefficient on t (the treatment indicator), why would changing the order of factor variables change the results. Is it not supposed to satisfy the additive property? Or am I missing something?