xtreg vs. reg: different result

[Peter Li]

I ran a model with fixed effects using the following two methods, and I expect the coefficient estimate for "treated" to be the same/similar.

But the results differ not insignificantly.

Method 1:

xi: reg lwage treated i.state i.year $controls, cluster(state)

	Robust
lwage	Coef.	Std. Err.	t	P>t	[95% Conf.	Interval]
treated	-.0545311	.012696	-4.30	0.000	-.0800446	-.0290176

Method 2:

xtset state year
xtreg lwage treated $controls, fe vce(cluster state)

	Robust
lwage	Coef.	Std. Err.	t	P>t	[95% Conf.	Interval]
treated	-.0669304	.0148743	-4.50	0.000	-.0968214	-.0370394

What is the reason for the difference? Or did I misspecify anything?


Thanks!

[FernandoRios]

The most likely explanation is that you didn't include year fixed effect in the second method. xtreg does not automatically include year fixed effects in the estimation.
HTH
Fernando

[Clyde Schechter]

These are two different models. The first one contains fixed effects for both state and year, but the second one contains only state effects.

When you -xtset- your data and use an -xt- estimator, you automatically get fixed effects for the panel variable. But you do not get fixed effects for the time variable unless you name them explicitly as variables in the regression command.

As an aside, the -xi- command is largely obsolete and you should more or less forget you ever knew it. It has been replaced by factor variable notation: see -help fvvarlist-. There are some Stata commands that still do not support factor variable notation and require the use of -xi-, but for the most part these are archaic commands that have, themselves, been largely replaced by modern commands that encompass the same calculations and do support factor variable notation. There are, admittedly, a handful of situations where -xi- is still useful and even the most modern commands do not allow factor-variable notation, but they are fairly exotic. So take up factor variable notation (which will allow you to make use of the wonderful -margins- command and will also simplify many regression model specifications) and tuck -xi- into a dusty back corner of your mind.

Added: Crossed with #2 which highlights the same problem.

[Peter Li]

FernandoRios Thank you! you're definitely right!


Clyde Schechter Thank you as always! Just an old habit I picked up from my professors. Will definitely keep it in mind!

[Peter Li]

Clyde Schechter May I follow up with this question? It now giving me very different results after I added a quadric stat-specific time trend:


Method1

reg lwage treated i.state i.year $controls i.state##c.year##c.year, cluster(state)

	Robust
lwage	Coef.	Std. Err.	t	P>t	[95% Conf.	Interval]
treated	.0261329	.0080116	3.26	0.002	.0100331	.0422328

Method2

xtreg lwage treated i.year $controls i.state##c.year##c.year, fe vce(cluster state)

	Robust
lwage	Coef.	Std. Err.	t	P>t	[95% Conf.	Interval]
treated	-.0382726	.0065913	-5.81	0.000	-.0515183	-.0250268

[Clyde Schechter]

I can't tell without seeing the complete output of both regressions.

[Peter Li]

Clyde Schechter It appears that OLS dropped quadratic term but kept state FE and linear trend, but xtreg dropped state FE but kept both interaction terms. Why is the choice of omitting variable differ?

Here is it. Sorry, the output is really long:

Method 1:

Linear regression                               Number of obs     =      1,250
                                                F(27, 49)         =          .
                                                Prob > F          =          .
                                                R-squared         =     0.9666
                                                Root MSE          =     .02982

                                        (Std. Err. adjusted for 50 clusters in state)
-------------------------------------------------------------------------------------
                    |               Robust
              lwage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------------+----------------------------------------------------------------
            treated |   .0261329   .0080116     3.26   0.002     .0100331    .0422328
                    |
              state |
                 2  |  -36.17335   2.212987   -16.35   0.000    -40.62052   -31.72619
                 3  |  -32.81572   1.312822   -25.00   0.000    -35.45393    -30.1775
                 4  |   .1126636   6.591338     0.02   0.986    -13.13313    13.35845
                 5  |  -24.25648   .4615767   -52.55   0.000    -25.18406   -23.32891
                 6  |  -19.95343   2.741324    -7.28   0.000    -25.46233   -14.44454
                 7  |  -44.12615   3.319284   -13.29   0.000    -50.79651    -37.4558
                 9  |  -25.69199   1.090259   -23.57   0.000    -27.88295   -23.50103
                10  |    -17.411   3.056654    -5.70   0.000    -23.55357   -11.26842
                11  |   -20.4717   3.008458    -6.80   0.000    -26.51742   -14.42597
                12  |  -26.79742   1.243872   -21.54   0.000    -29.29707   -24.29776
                13  |  -42.07455   3.861682   -10.90   0.000    -49.83489   -34.31421
                14  |  -17.95453   2.543017    -7.06   0.000    -23.06492   -12.84415
                15  |  -35.01909   2.906898   -12.05   0.000    -40.86072   -29.17746
                16  |  -39.69767   2.388112   -16.62   0.000    -44.49676   -34.89858
                17  |  -32.24021   2.443834   -13.19   0.000    -37.15128   -27.32914
                18  |  -37.80227   2.490811   -15.18   0.000    -42.80774   -32.79679
                19  |  -33.60808   4.367692    -7.69   0.000    -42.38529   -24.83087
                20  |  -44.51344   3.127703   -14.23   0.000    -50.79879   -38.22808
                21  |   -39.7398   .9004826   -44.13   0.000    -41.54939   -37.93021
                22  |  -43.54108    2.90684   -14.98   0.000     -49.3826   -37.69957
                23  |  -36.38179   3.046798   -11.94   0.000    -42.50457   -30.25902
                24  |  -37.54612   1.405976   -26.70   0.000    -40.37154   -34.72071
                25  |  -34.99252   2.158804   -16.21   0.000     -39.3308   -30.65424
                26  |  -33.04157   2.477448   -13.34   0.000    -38.02019   -28.06295
                27  |  -23.39811   2.250302   -10.40   0.000    -27.92026   -18.87596
                28  |   -25.1828   1.497547   -16.82   0.000    -28.19224   -22.17337
                29  |  -35.00125   5.458408    -6.41   0.000    -45.97033   -24.03217
                30  |  -39.78949   2.791518   -14.25   0.000    -45.39926   -34.17972
                31  |  -33.77585   1.194775   -28.27   0.000    -36.17684   -31.37486
                32  |  -39.27935   2.500898   -15.71   0.000    -44.30509   -34.25361
                33  |  -15.99187   .9770817   -16.37   0.000    -17.95539   -14.02835
                34  |   19.67458   12.16311     1.62   0.112     -4.76811    44.11727
                35  |  -39.72666   3.485097   -11.40   0.000    -46.73023    -32.7231
                36  |  -35.13634   3.746491    -9.38   0.000     -42.6652   -27.60749
                37  |  -20.28686   3.438414    -5.90   0.000    -27.19661   -13.37711
                38  |  -21.17755   1.128087   -18.77   0.000    -23.44453   -18.91058
                39  |  -40.34164   4.118247    -9.80   0.000    -48.61757   -32.06572
                40  |  -43.41494   2.978145   -14.58   0.000    -49.39975   -37.43013
                41  |  -29.95618   .6826219   -43.88   0.000    -31.32796    -28.5844
                42  |  -39.80805   2.587202   -15.39   0.000    -45.00723   -34.60888
                43  |  -37.92873   .8776665   -43.22   0.000    -39.69246   -36.16499
                44  |  -12.80051   1.473255    -8.69   0.000    -15.76113   -9.839891
                45  |  -12.21771   3.321052    -3.68   0.001    -18.89161   -5.543802
                46  |   -37.1673   .7448545   -49.90   0.000    -38.66414   -35.67046
                47  |  -36.91803   1.923683   -19.19   0.000    -40.78382   -33.05225
                48  |  -22.22552   1.646785   -13.50   0.000    -25.53486   -18.91618
                49  |    -37.464   2.101323   -17.83   0.000    -41.68677   -33.24124
                50  |  -35.64333   5.573101    -6.40   0.000     -46.8429   -24.44376
                51  |  -27.93493   4.038321    -6.92   0.000    -36.05024   -19.81962
                    |
               year |
              1984  |  -.0275687   .0040007    -6.89   0.000    -.0356084   -.0195289
              1985  |  -.0273947   .0052437    -5.22   0.000    -.0379323   -.0168572
              1986  |    .000998   .0075081     0.13   0.895    -.0140901     .016086
              1987  |  -.0062596   .0081249    -0.77   0.445    -.0225871    .0100679
              1988  |  -.0345376   .0095563    -3.61   0.001    -.0537417   -.0153335
              1989  |  -.1131549   .0092166   -12.28   0.000    -.1316763   -.0946334
              1990  |  -.1327157   .0097714   -13.58   0.000     -.152352   -.1130794
              1991  |  -.1618562   .0090928   -17.80   0.000    -.1801288   -.1435836
              1992  |  -.1850898   .0098986   -18.70   0.000    -.2049818   -.1651979
              1993  |  -.1932918   .0112056   -17.25   0.000    -.2158103   -.1707733
              1994  |  -.3275327   .0106313   -30.81   0.000    -.3488971   -.3061683
              1995  |  -.3391742   .0107399   -31.58   0.000    -.3607569   -.3175916
              1996  |  -.2293491   .0109222   -21.00   0.000     -.251298   -.2074002
              1997  |  -.2123682    .010313   -20.59   0.000    -.2330928   -.1916435
              1998  |  -.1740775    .011341   -15.35   0.000     -.196868   -.1512869
              1999  |  -.1771014   .0117066   -15.13   0.000    -.2006267   -.1535761
              2000  |  -.3036969   .0117285   -25.89   0.000    -.3272661   -.2801276
              2001  |  -.2821368   .0114236   -24.70   0.000    -.3050934   -.2591802
              2002  |  -.2601558   .0121684   -21.38   0.000     -.284609   -.2357025
              2003  |  -.2452815   .0129979   -18.87   0.000    -.2714018   -.2191611
              2004  |  -.2893418   .0138559   -20.88   0.000    -.3171862   -.2614974
              2005  |  -.4133361   .0126078   -32.78   0.000    -.4386724   -.3879997
              2006  |  -.4268682   .0141236   -30.22   0.000    -.4552505   -.3984858
              2007  |  -.4307693   .0145098   -29.69   0.000    -.4599279   -.4016106
                    |
            college |   .0047768   .0006991     6.83   0.000     .0033719    .0061817
              metro |   .0000423   .0001489     0.28   0.777    -.0002568    .0003415
               male |   .0014856   .0010942     1.36   0.181    -.0007133    .0036845
              white |  -.0010569   .0009324    -1.13   0.262    -.0029306    .0008167
               lpop |   .6443217   .1784324     3.61   0.001     .2857483    1.002895
              lmile |          0  (omitted)
         rtw_states |          0  (omitted)
                    |
       state#c.year |
                 1  |  -.0139132   .0020435    -6.81   0.000    -.0180197   -.0098068
                 2  |   .0034129   .0013688     2.49   0.016     .0006621    .0061636
                 3  |   .0018641   .0016217     1.15   0.256    -.0013949    .0051231
                 4  |  -.0147191   .0054156    -2.72   0.009    -.0256023    -.003836
                 5  |  -.0030787   .0024375    -1.26   0.213     -.007977    .0018195
                 6  |  -.0045827   .0034289    -1.34   0.188    -.0114733    .0023079
                 7  |   .0076437   .0008598     8.89   0.000     .0059159    .0093715
                 9  |  -.0011775   .0025637    -0.46   0.648    -.0063294    .0039745
                10  |  -.0063584   .0037329    -1.70   0.095    -.0138599    .0011432
                11  |  -.0045867   .0037263    -1.23   0.224     -.012075    .0029015
                12  |  -.0008401   .0015213    -0.55   0.583    -.0038973    .0022171
                13  |    .006505    .000629    10.34   0.000      .005241    .0077689
                14  |  -.0052954   .0031735    -1.67   0.102    -.0116727     .001082
                15  |   .0026001   .0010497     2.48   0.017     .0004907    .0047095
                16  |   .0051237   .0011794     4.34   0.000     .0027536    .0074938
                17  |   .0016329   .0011065     1.48   0.146    -.0005907    .0038564
                18  |   .0042703   .0010979     3.89   0.000     .0020639    .0064767
                19  |    .002133   .0008746     2.44   0.018     .0003753    .0038906
                20  |    .007609   .0010244     7.43   0.000     .0055505    .0096675
                21  |   .0052619   .0019619     2.68   0.010     .0013194    .0092044
                22  |   .0075162   .0007361    10.21   0.000     .0060369    .0089955
                23  |   .0033459   .0010144     3.30   0.002     .0013075    .0053843
                24  |    .004164   .0017129     2.43   0.019     .0007218    .0076062
                25  |   .0027783   .0012899     2.15   0.036     .0001862    .0053703
                26  |   .0019426   .0010803     1.80   0.078    -.0002282    .0041135
                27  |  -.0025211   .0010326    -2.44   0.018    -.0045962    -.000446
                28  |  -.0022509   .0029135    -0.77   0.443    -.0081057    .0036039
                29  |   .0033965   .0008736     3.89   0.000     .0016408    .0051521
                30  |   .0055316   .0008349     6.63   0.000     .0038537    .0072094
                31  |   .0027405   .0020428     1.34   0.186    -.0013647    .0068456
                32  |   .0049305   .0013048     3.78   0.000     .0023085    .0075525
                33  |  -.0063947   .0025226    -2.53   0.014    -.0114641   -.0013253
                34  |  -.0241798   .0081089    -2.98   0.004    -.0404751   -.0078844
                35  |   .0048407   .0008901     5.44   0.000     .0030521    .0066294
                36  |   .0026411   .0007514     3.51   0.001      .001131    .0041512
                37  |  -.0044607   .0009397    -4.75   0.000     -.006349   -.0025723
                38  |  -.0039421   .0025961    -1.52   0.135    -.0091592    .0012749
                39  |   .0052364   .0006986     7.50   0.000     .0038325    .0066402
                40  |   .0075736   .0009112     8.31   0.000     .0057424    .0094048
                41  |   .0003408   .0021817     0.16   0.877    -.0040434    .0047251
                42  |    .005761   .0008264     6.97   0.000     .0041003    .0074216
                43  |   .0042358   .0020712     2.05   0.046     .0000736    .0083979
                44  |  -.0087242   .0029434    -2.96   0.005    -.0146392   -.0028093
                45  |   -.008316   .0036498    -2.28   0.027    -.0156506   -.0009814
                46  |   .0038452   .0022823     1.68   0.098    -.0007413    .0084316
                47  |   .0044624   .0012987     3.44   0.001     .0018526    .0070722
                48  |  -.0035475   .0029719    -1.19   0.238    -.0095196    .0024247
                49  |   .0040496   .0012795     3.16   0.003     .0014783    .0066208
                50  |    .003412   .0009316     3.66   0.001     .0015399    .0052842
                51  |          0  (omitted)
                    |
state#c.year#c.year |
                 1  |          0  (omitted)
                 2  |          0  (omitted)
                 3  |          0  (omitted)
                 4  |          0  (omitted)
                 5  |          0  (omitted)
                 6  |          0  (omitted)
                 7  |          0  (omitted)
                 9  |          0  (omitted)
                10  |          0  (omitted)
                11  |          0  (omitted)
                12  |          0  (omitted)
                13  |          0  (omitted)
                14  |          0  (omitted)
                15  |          0  (omitted)
                16  |          0  (omitted)
                17  |          0  (omitted)
                18  |          0  (omitted)
                19  |          0  (omitted)
                20  |          0  (omitted)
                21  |          0  (omitted)
                22  |          0  (omitted)
                23  |          0  (omitted)
                24  |          0  (omitted)
                25  |          0  (omitted)
                26  |          0  (omitted)
                27  |          0  (omitted)
                28  |          0  (omitted)
                29  |          0  (omitted)
                30  |          0  (omitted)
                31  |          0  (omitted)
                32  |          0  (omitted)
                33  |          0  (omitted)
                34  |          0  (omitted)
                35  |          0  (omitted)
                36  |          0  (omitted)
                37  |          0  (omitted)
                38  |          0  (omitted)
                39  |          0  (omitted)
                40  |          0  (omitted)
                41  |          0  (omitted)
                42  |          0  (omitted)
                43  |          0  (omitted)
                44  |          0  (omitted)
                45  |          0  (omitted)
                46  |          0  (omitted)
                47  |          0  (omitted)
                48  |          0  (omitted)
                49  |          0  (omitted)
                50  |          0  (omitted)
                51  |          0  (omitted)
                    |
              _cons |   22.35667   2.062577    10.84   0.000     18.21177    26.50157
-------------------------------------------------------------------------------------

Method 2:

Fixed-effects (within) regression               Number of obs     =      1,250
Group variable: state                           Number of groups  =         50

R-sq:                                           Obs per group:
     within  = 0.9229                                         min =         25
     between = 0.0002                                         avg =       25.0
     overall = 0.0001                                         max =         25

                                                F(17,49)          =          .
corr(u_i, Xb)  = -1.0000                        Prob > F          =          .

                                        (Std. Err. adjusted for 50 clusters in state)
-------------------------------------------------------------------------------------
                    |               Robust
              lwage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------------+----------------------------------------------------------------
            treated |  -.0382726   .0065913    -5.81   0.000    -.0515183   -.0250268
                    |
               year |
              1984  |  -.0555126   .0046313   -11.99   0.000    -.0648196   -.0462056
              1985  |  -.0815403   .0077592   -10.51   0.000    -.0971329   -.0659476
              1986  |  -.0785557   .0093123    -8.44   0.000    -.0972693    -.059842
              1987  |   -.110025   .0119546    -9.20   0.000    -.1340487   -.0860013
              1988  |  -.1610242   .0141427   -11.39   0.000     -.189445   -.1326035
              1989  |  -.2618081   .0148638   -17.61   0.000     -.291678   -.2319382
              1990  |  -.3021409   .0173573   -17.41   0.000    -.3370217   -.2672601
              1991  |  -.3512706   .0204661   -17.16   0.000    -.3923987   -.3101425
              1992  |  -.3934975      .0243   -16.19   0.000    -.4423302   -.3446648
              1993  |  -.4196494   .0283423   -14.81   0.000    -.4766055   -.3626934
              1994  |  -.5700363   .0307412   -18.54   0.000     -.631813   -.5082595
              1995  |  -.5970559    .034102   -17.51   0.000    -.6655863   -.5285254
              1996  |  -.5020133   .0371361   -13.52   0.000     -.576641   -.4273855
              1997  |  -.4976747   .0391774   -12.70   0.000    -.5764047   -.4189448
              1998  |  -.4712658   .0416107   -11.33   0.000    -.5548856   -.3876459
              1999  |  -.4850141   .0432868   -11.20   0.000    -.5720022    -.398026
              2000  |  -.6209284   .0460284   -13.49   0.000     -.713426   -.5284309
              2001  |   -.604501   .0489043   -12.36   0.000    -.7027779   -.5062241
              2002  |  -.5895634   .0501188   -11.76   0.000    -.6902809   -.4888459
              2003  |  -.5801771   .0530559   -10.94   0.000    -.6867969   -.4735572
              2004  |   -.628801   .0547053   -11.49   0.000    -.7387355   -.5188665
              2005  |  -.7564063   .0549042   -13.78   0.000    -.8667405   -.6460722
              2006  |  -.7723675   .0591109   -13.07   0.000    -.8911552   -.6535798
              2007  |  -.7776052   .0608049   -12.79   0.000    -.8997974   -.6554131
                    |
            college |   .0049949   .0006564     7.61   0.000     .0036758     .006314
              metro |   .0001374    .000134     1.03   0.310     -.000132    .0004067
               male |   .0018616    .001013     1.84   0.072     -.000174    .0038973
              white |  -.0005209   .0007364    -0.71   0.483    -.0020007    .0009589
               lpop |   .7204224   .2035838     3.54   0.001     .3113055    1.129539
              lmile |          0  (omitted)
         rtw_states |          0  (omitted)
                    |
              state |
                 2  |          0  (omitted)
                 3  |          0  (omitted)
                 4  |          0  (omitted)
                 5  |          0  (omitted)
                 6  |          0  (omitted)
                 7  |          0  (omitted)
                 9  |          0  (omitted)
                10  |          0  (omitted)
                11  |          0  (omitted)
                12  |          0  (omitted)
                13  |          0  (omitted)
                14  |          0  (omitted)
                15  |          0  (omitted)
                16  |          0  (omitted)
                17  |          0  (omitted)
                18  |          0  (omitted)
                19  |          0  (omitted)
                20  |          0  (omitted)
                21  |          0  (omitted)
                22  |          0  (omitted)
                23  |          0  (omitted)
                24  |          0  (omitted)
                25  |          0  (omitted)
                26  |          0  (omitted)
                27  |          0  (omitted)
                28  |          0  (omitted)
                29  |          0  (omitted)
                30  |          0  (omitted)
                31  |          0  (omitted)
                32  |          0  (omitted)
                33  |          0  (omitted)
                34  |          0  (omitted)
                35  |          0  (omitted)
                36  |          0  (omitted)
                37  |          0  (omitted)
                38  |          0  (omitted)
                39  |          0  (omitted)
                40  |          0  (omitted)
                41  |          0  (omitted)
                42  |          0  (omitted)
                43  |          0  (omitted)
                44  |          0  (omitted)
                45  |          0  (omitted)
                46  |          0  (omitted)
                47  |          0  (omitted)
                48  |          0  (omitted)
                49  |          0  (omitted)
                50  |          0  (omitted)
                51  |          0  (omitted)
                    |
               year |          0  (omitted)
                    |
       state#c.year |
                 2  |   1.936379   .1852959    10.45   0.000     1.564013    2.308745
                 3  |   1.503604   .2436426     6.17   0.000     1.013986    1.993223
                 4  |   2.148227   .2085051    10.30   0.000      1.72922    2.567234
                 5  |   .2986172   .2741777     1.09   0.281    -.2523634    .8495978
                 6  |   1.172371   .2817482     4.16   0.000     .6061766    1.738565
                 7  |   3.833253   .1800583    21.29   0.000     3.471412    4.195093
                 9  |    2.23056   .2370954     9.41   0.000     1.754099    2.707021
                10  |   1.966684   .1655509    11.88   0.000     1.633996    2.299371
                11  |   2.935132   .2015799    14.56   0.000     2.530042    3.340222
                12  |   3.521044   .2903489    12.13   0.000     2.937566    4.104522
                13  |   2.573466   .2724581     9.45   0.000     2.025941    3.120991
                14  |    3.70418   .4213648     8.79   0.000     2.857416    4.550944
                15  |   2.845735   .2141673    13.29   0.000      2.41535     3.27612
                16  |   3.941566   .2498288    15.78   0.000     3.439516    4.443615
                17  |   .8267457   .1889731     4.37   0.000     .4469901    1.206501
                18  |   3.063922   .2807597    10.91   0.000     2.499714    3.628129
                19  |   .6329119   .2607301     2.43   0.019     .1089551    1.156869
                20  |   3.495603   .1956781    17.86   0.000     3.102373    3.888832
                21  |    2.55316    .161244    15.83   0.000     2.229128    2.877192
                22  |   3.265805    .372694     8.76   0.000     2.516849    4.014762
                23  |   3.059204    .147253    20.78   0.000     2.763288     3.35512
                24  |   1.570282   .1674856     9.38   0.000     1.233707    1.906857
                25  |   2.349027   .2270627    10.35   0.000     1.892728    2.805327
                26  |   3.150521   .2387243    13.20   0.000     2.670787    3.630256
                27  |   1.308291   .4172618     3.14   0.003     .4697714     2.14681
                28  |   3.839569   .2090104    18.37   0.000     3.419547    4.259592
                29  |   1.002939   .4194477     2.39   0.021     .1600271     1.84585
                30  |   3.539309   .2922946    12.11   0.000     2.951921    4.126697
                31  |   2.155773   .3748046     5.75   0.000     1.402575    2.908971
                32  |   3.089361   .1574736    19.62   0.000     2.772905    3.405816
                33  |   .4543869   .1983973     2.29   0.026     .0556926    .8530812
                34  |   1.394732   .2845823     4.90   0.000     .8228425    1.966621
                35  |   3.833486   .1920646    19.96   0.000     3.447518    4.219454
                36  |   2.890463    .167575    17.25   0.000     2.553708    3.227217
                37  |   .1638388   .4564164     0.36   0.721    -.7533643    1.081042
                38  |   1.938984   .2376574     8.16   0.000     1.461394    2.416575
                39  |   3.466286   .1776292    19.51   0.000     3.109326    3.823245
                40  |   3.644357   .2288685    15.92   0.000     3.184428    4.104285
                41  |   3.878219   .2198538    17.64   0.000     3.436407    4.320032
                42  |   3.374835   .3585027     9.41   0.000     2.654397    4.095273
                43  |   3.393864   .2208026    15.37   0.000     2.950145    3.837584
                44  |    1.70279   .2981333     5.71   0.000     1.103669    2.301912
                45  |   2.523345   .3107388     8.12   0.000     1.898892    3.147798
                46  |   1.302569   .2042889     6.38   0.000      .892035    1.713103
                47  |   3.089797   .1794328    17.22   0.000     2.729213     3.45038
                48  |   .5129477     .27603     1.86   0.069    -.0417554    1.067651
                49  |   2.574496   .2281925    11.28   0.000     2.115926    3.033066
                50  |   2.578907   .3408982     7.57   0.000     1.893846    3.263967
                51  |    .720812   .6215035     1.16   0.252    -.5281461     1.96977
                    |
      c.year#c.year |          0  (omitted)
                    |
state#c.year#c.year |
                 2  |  -.0004809   .0000464   -10.37   0.000    -.0005741   -.0003877
                 3  |  -.0003729    .000061    -6.12   0.000    -.0004954   -.0002504
                 4  |   -.000539   .0000523   -10.30   0.000    -.0006442   -.0004338
                 5  |  -.0000722   .0000686    -1.05   0.298    -.0002101    .0000657
                 6  |  -.0002918   .0000709    -4.11   0.000    -.0004343   -.0001492
                 7  |  -.0009552   .0000449   -21.25   0.000    -.0010455   -.0008649
                 9  |  -.0005559   .0000594    -9.36   0.000    -.0006753   -.0004365
                10  |  -.0004913   .0000412   -11.92   0.000    -.0005741   -.0004085
                11  |  -.0007335   .0000509   -14.42   0.000    -.0008357   -.0006313
                12  |  -.0008792   .0000728   -12.07   0.000    -.0010255   -.0007328
                13  |  -.0006398    .000068    -9.41   0.000    -.0007763   -.0005032
                14  |  -.0009264   .0001058    -8.76   0.000     -.001139   -.0007138
                15  |   -.000709   .0000535   -13.25   0.000    -.0008165   -.0006015
                16  |  -.0009831   .0000625   -15.73   0.000    -.0011087   -.0008575
                17  |  -.0002033   .0000473    -4.30   0.000    -.0002983   -.0001082
                18  |  -.0007633   .0000701   -10.88   0.000    -.0009042   -.0006224
                19  |  -.0001544    .000065    -2.38   0.021     -.000285   -.0000238
                20  |  -.0008706   .0000489   -17.80   0.000    -.0009689   -.0007723
                21  |  -.0006351   .0000405   -15.70   0.000    -.0007164   -.0005538
                22  |   -.000813   .0000934    -8.70   0.000    -.0010008   -.0006253
                23  |  -.0007623   .0000369   -20.65   0.000    -.0008365   -.0006881
                24  |  -.0003891    .000042    -9.27   0.000    -.0004734   -.0003047
                25  |  -.0005845   .0000568   -10.30   0.000    -.0006986   -.0004704
                26  |  -.0007855   .0000597   -13.17   0.000    -.0009054   -.0006657
                27  |   -.000325   .0001044    -3.11   0.003    -.0005349   -.0001151
                28  |  -.0009596   .0000526   -18.25   0.000    -.0010652   -.0008539
                29  |  -.0002468   .0001048    -2.35   0.023    -.0004574   -.0000361
                30  |  -.0008821   .0000731   -12.07   0.000    -.0010289   -.0007352
                31  |  -.0005362   .0000939    -5.71   0.000    -.0007249   -.0003475
                32  |  -.0007695   .0000394   -19.55   0.000    -.0008486   -.0006904
                33  |  -.0001121   .0000497    -2.25   0.029     -.000212   -.0000122
                34  |  -.0003528     .00007    -5.04   0.000    -.0004936   -.0002121
                35  |   -.000956   .0000479   -19.94   0.000    -.0010523   -.0008596
                36  |  -.0007202   .0000419   -17.20   0.000    -.0008043    -.000636
                37  |  -.0000378   .0001141    -0.33   0.742    -.0002672    .0001916
                38  |  -.0004836   .0000595    -8.12   0.000    -.0006032    -.000364
                39  |  -.0008638   .0000443   -19.50   0.000    -.0009529   -.0007748
                40  |  -.0009079   .0000574   -15.82   0.000    -.0010233   -.0007926
                41  |  -.0009685   .0000551   -17.58   0.000    -.0010792   -.0008578
                42  |  -.0008408   .0000897    -9.37   0.000    -.0010211   -.0006605
                43  |  -.0008461   .0000554   -15.28   0.000    -.0009574   -.0007348
                44  |  -.0004256   .0000749    -5.68   0.000    -.0005762    -.000275
                45  |  -.0006313   .0000783    -8.07   0.000    -.0007885    -.000474
                46  |  -.0003221   .0000512    -6.29   0.000     -.000425   -.0002192
                47  |  -.0007698   .0000451   -17.05   0.000    -.0008605   -.0006791
                48  |  -.0001261    .000069    -1.83   0.074    -.0002647    .0000125
                49  |  -.0006407   .0000572   -11.20   0.000    -.0007557   -.0005258
                50  |  -.0006418   .0000848    -7.57   0.000    -.0008122   -.0004714
                51  |  -.0001769   .0001553    -1.14   0.260     -.000489    .0001351
                    |
              _cons |  -2354.992   203.9645   -11.55   0.000    -2764.874    -1945.11
--------------------+----------------------------------------------------------------
            sigma_u |  1153.5661
            sigma_e |  .02713741
                rho |          1   (fraction of variance due to u_i)
-------------------------------------------------------------------------------------

[Clyde Schechter]

The method by which Stata chooses which effects to omit when confronted with collinearity is not described in the documentation, and if you try to pursue it in the code, you find out that it is buried in machine-language code, and so, inaccessible to users. So the answer to your question why the two routines do it differently is, I don't know.

But here's the important thing to understand is that once you have a big collinearity like this, none of the involved parameters is identifiable: they are simply artifacts of the particular way in which the collinearity is removed by imposing constraints (omissions of variables).

Now, there is one thing you can do to reduce the collinearity here. Although from a strictly algebraic point of view, year, and year² are not colinear, from a practical perspective, taking into account rounding and precision, they are. So you will have fewer things dropped if you center the continuous year variable. -gen year_centered = year - 1999- and then use c.year_centered##c.year_centered instead of c.year##c.year. You will still have some collinearities and this may still affect the estimate of treated--but if so that is because treated is itself involved in the collinearity so that its effect cannot be estimated. You have to simplify the model eliminating extraneous terms until you have no variables omitted except for the base category of each categorical variable.

This may well mean that you will not be able to have both i.year and a quadratic model for year. If you think about it, given both the continuous value of year and an indicator for each separate year, you can calculate year^2 by assigning an appropriate coefficient to each year indicator (namely the value of the year itself). So you will need to think about which representation makes more sense for your purposes.

[Peter Li]

This makes so much sense now, thanks Clyde!