Dear All, I make up this data set.
Code:
* Example generated by -dataex-. For more info, type help dataex
clear
input long id float(year y x GDP) byte(id1 id2 id3 id4 year1 year2 year3 year4)
1 2011  1.477398  .3132002 5.3 1 0 0 0 1 0 0 0
1 2012 1.7059364 .55597913 6.2 1 0 0 0 0 1 0 0
1 2013 2.2016048  .9382851 7.5 1 0 0 0 0 0 1 0
1 2014 2.3101015  .7363221 7.8 1 0 0 0 0 0 0 1
2 2011  .4857773 .19240755 5.3 0 1 0 0 1 0 0 0
2 2012  1.192688 .19514006 6.2 0 1 0 0 0 1 0 0
2 2013 2.0814517  .9509598 7.5 0 1 0 0 0 0 1 0
2 2014  .6230519 .29044542 7.8 0 1 0 0 0 0 0 1
3 2011 2.2117586  .8190824 5.3 0 0 1 0 1 0 0 0
3 2012 1.8595012  .4882096 6.2 0 0 1 0 0 1 0 0
3 2013  1.259727 .27048662 7.5 0 0 1 0 0 0 1 0
3 2014 1.4586093 .58597064 7.8 0 0 1 0 0 0 0 1
4 2011 .10921151 .05390351 5.3 0 0 0 1 1 0 0 0
4 2012 2.0568795  .5583192 6.2 0 0 0 1 0 1 0 0
4 2013 1.7943153  .6395468 7.5 0 0 0 1 0 0 1 0
4 2014  2.802899  .9747689 7.8 0 0 0 1 0 0 0 1
end
Note that GDP is perfectly correlated with year dummies year1, year2, year3, and year4. Thus, their coefficients are not identified.
however, I run the following regressions and obtain corresponding results:
Code:
. // LSDV
. reg y x GDP i.id i.year, robust
note: 2014.year omitted because of collinearity

Linear regression                               Number of obs     =         16
                                                F(7, 8)           =      11.60
                                                Prob > F          =     0.0013
                                                R-squared         =     0.8951
                                                Root MSE          =     .32347

------------------------------------------------------------------------------
             |               Robust
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           x |    2.17054   .3308689     6.56   0.000     1.407555    2.933525
         GDP |   .0286521   .0887787     0.32   0.755    -.1760719    .2333761
             |
          id |
          2  |  -.3315972    .250505    -1.32   0.222    -.9092628    .2460684
          3  |  -.0201396   .2505058    -0.08   0.938     -.597807    .5575277
          4  |   -.060784    .265267    -0.23   0.825    -.6724908    .5509228
             |
        year |
       2012  |   .3795345    .203945     1.86   0.100    -.0907635    .8498324
       2013  |  -.0707095   .2083043    -0.34   0.743    -.5510601    .4096412
       2014  |          0  (omitted)
             |
       _cons |   .2742371   .7161895     0.38   0.712    -1.377299    1.925773
------------------------------------------------------------------------------

. reg y x GDP i.id year1-year4, robust
note: year3 omitted because of collinearity
note: year4 omitted because of collinearity

Linear regression                               Number of obs     =         16
                                                F(7, 8)           =      11.60
                                                Prob > F          =     0.0013
                                                R-squared         =     0.8951
                                                Root MSE          =     .32347

------------------------------------------------------------------------------
             |               Robust
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           x |    2.17054   .3308689     6.56   0.000     1.407555    2.933525
         GDP |   .2643503   .7322967     0.36   0.727    -1.424329     1.95303
             |
          id |
          2  |  -.3315972    .250505    -1.32   0.222    -.9092628    .2460684
          3  |  -.0201396   .2505058    -0.08   0.938     -.597807    .5575277
          4  |   -.060784    .265267    -0.23   0.825    -.6724908    .5509228
             |
       year1 |   .5892453   1.735868     0.34   0.743    -3.413674    4.592165
       year2 |   .7566516   1.081587     0.70   0.504    -1.737492    3.250795
       year3 |          0  (omitted)
       year4 |          0  (omitted)
       _cons |  -1.564208    5.68777    -0.28   0.790    -14.68023    11.55181
------------------------------------------------------------------------------

. 
. reg y x GDP i.id year2 year3 year4, robust
note: year4 omitted because of collinearity

Linear regression                               Number of obs     =         16
                                                F(7, 8)           =      11.60
                                                Prob > F          =     0.0013
                                                R-squared         =     0.8951
                                                Root MSE          =     .32347

------------------------------------------------------------------------------
             |               Robust
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           x |    2.17054   .3308689     6.56   0.000     1.407555    2.933525
         GDP |   .0286521   .0887787     0.32   0.755    -.1760719    .2333761
             |
          id |
          2  |  -.3315972    .250505    -1.32   0.222    -.9092628    .2460684
          3  |  -.0201396   .2505058    -0.08   0.938     -.597807    .5575277
          4  |   -.060784    .265267    -0.23   0.825    -.6724908    .5509228
             |
       year2 |   .3795345    .203945     1.86   0.100    -.0907635    .8498324
       year3 |  -.0707095   .2083043    -0.34   0.743    -.5510601    .4096412
       year4 |          0  (omitted)
       _cons |   .2742371   .7161895     0.38   0.712    -1.377299    1.925773
------------------------------------------------------------------------------

. reg y x GDP i.id year3 year4 year2, robust
note: year2 omitted because of collinearity

Linear regression                               Number of obs     =         16
                                                F(7, 8)           =      11.60
                                                Prob > F          =     0.0013
                                                R-squared         =     0.8951
                                                Root MSE          =     .32347

------------------------------------------------------------------------------
             |               Robust
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           x |    2.17054   .3308689     6.56   0.000     1.407555    2.933525
         GDP |   .4503573   .2562406     1.76   0.117    -.1405346    1.041249
             |
          id |
          2  |  -.3315972    .250505    -1.32   0.222    -.9092628    .2460684
          3  |  -.0201396   .2505058    -0.08   0.938     -.597807    .5575277
          4  |   -.060784    .265267    -0.23   0.825    -.6724908    .5509228
             |
       year3 |  -.9984607   .4933028    -2.02   0.078    -2.136019    .1390975
       year4 |  -1.054263   .5665141    -1.86   0.100    -2.360647    .2521209
       year2 |          0  (omitted)
       _cons |    -1.9608   1.567078    -1.25   0.246     -5.57449    1.652889
------------------------------------------------------------------------------

. reg y x GDP i.id year4 year2 year3, robust
note: year3 omitted because of collinearity

Linear regression                               Number of obs     =         16
                                                F(7, 8)           =      11.60
                                                Prob > F          =     0.0013
                                                R-squared         =     0.8951
                                                Root MSE          =     .32347

------------------------------------------------------------------------------
             |               Robust
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           x |    2.17054   .3308689     6.56   0.000     1.407555    2.933525
         GDP |  -.0034885    .102658    -0.03   0.974    -.2402184    .2332413
             |
          id |
          2  |  -.3315972    .250505    -1.32   0.222    -.9092628    .2460684
          3  |  -.0201396   .2505058    -0.08   0.938     -.597807    .5575277
          4  |   -.060784    .265267    -0.23   0.825    -.6724908    .5509228
             |
       year4 |   .0803517   .2367095     0.34   0.743    -.4655014    .6262048
       year2 |   .4084611   .2018056     2.02   0.078    -.0569035    .8738257
       year3 |          0  (omitted)
       _cons |   .4445827   .7297813     0.61   0.559    -1.238296    2.127461
------------------------------------------------------------------------------
My questions are: (1) Is there a rule for Stata to delete certain variables before the estimation? (2). I know that year dummies are also perfectly correlated with the constant, so at least one year dummy has to be dropped. However, I also notice that at least one coefficient for the other dummies is zero. I doubt that it is because of GDP, but do know why? Any suggestions are highly appreciated.