Dropped variables due to multicollinearity using FE

[Karl Schneider]

Hi all. I am working on a panel data set, and I am currently trying to run a fixed effects model to look at the effect of different state types on crime (more complicated than that). My regression/specification information is as follows, attempting to control for fixed effects of state/year variation:
xtset districtid year
xtreg Crime StateType i.Year i.stateid, robust fe

However, whenever I run this regression, I continually encounter stateid and year variables being omitted due to multicollinearity. What recommendations would you have to try to circumvent this issue? Such issues do not occur using regular nor random effects. Thanks for your help.

[Andrew Musau]

Because districts are within states, it is unnecessary to have state dummies in the presence of district dummies. Consider this simple example

. webuse grunfeld

. summarize

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
     company |        200         5.5    2.879489          1         10
        year |        200      1944.5    5.780751       1935       1954
      invest |        200    145.9583    216.8753        .93     1486.7
      mvalue |        200    1081.681     1314.47      58.12     6241.7
      kstock |        200    276.0172    301.1039         .8     2226.3
-------------+---------------------------------------------------------
        time |        200        10.5    5.780751          1         20

Here, we have 10 companies. Let us suppose that companies 1 and 2 are in industry 1, companies 3 and 4 are in industry 2, and so on. I will generate an industry variable and run the same fixed effect regression as you do

. gen industry = 1 if inlist(company,1,2)
(160 missing values generated)

. replace industry = 2 if inlist(company,3,4)
(40 real changes made)

. replace industry = 3 if inlist(company,5,6)
(40 real changes made)

. replace industry = 4 if inlist(company,7,8)
(40 real changes made)

. replace industry = 5 if inlist(company,9,10)
(40 real changes made)

. xtset company year
       panel variable:  company (strongly balanced)
        time variable:  year, 1935 to 1954
                delta:  1 year


. xtreg mvalue kstock invest i.industry i.year, robust fe
note: 2.industry omitted because of collinearity
note: 3.industry omitted because of collinearity
note: 4.industry omitted because of collinearity
note: 5.industry omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =        200
Group variable: company                         Number of groups  =         10

R-sq:                                           Obs per group:
     within  = 0.5724                                         min =         20
     between = 0.7834                                         avg =       20.0
     overall = 0.6921                                         max =         20

                                                F(9,9)            =

     .
corr(u_i, Xb)  = 0.6529                         Prob > F          =          .

                               (Std. Err. adjusted for 10 clusters in company)
------------------------------------------------------------------------------
             |               Robust
      mvalue |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      kstock |  -.5884724   .4346371    -1.35   0.209     -1.57169     .394745
      invest |   2.569399   .8737022     2.94   0.016     .5929475    4.545851
             |
    industry |
          2  |          0  (omitted)
          3  |          0  (omitted)
          4  |          0  (omitted)
          5  |          0  (omitted)
             |
        year |
       1936  |   304.9451   144.9242     2.10   0.065    -22.89626    632.7865
       1937  |   540.9025   239.3157     2.26   0.050     -.467226    1082.272
       1938  |   172.6836   92.02179     1.88   0.093    -35.48414    380.8514
       1939  |   407.6552   168.1835     2.42   0.038     27.19764    788.1128
       1940  |   379.2305   149.0792     2.54   0.032     41.98991    716.4712
       1941  |   275.7897   115.5928     2.39   0.041     14.30065    537.2787
       1942  |   128.3897   52.69002     2.44   0.038     9.196569    247.5828
       1943  |   260.9976   94.88733     2.75   0.022      46.3475    475.6476
       1944  |    284.593   103.6925     2.74   0.023     50.02424    519.1618
       1945  |    392.883    147.817     2.66   0.026     58.49768    727.2684
       1946  |   369.6591   123.3859     3.00   0.015      90.5407    648.7775
       1947  |   173.2198   78.96076     2.19   0.056    -5.401875    351.8414
       1948  |   149.5766   115.3639     1.30   0.227    -111.3946    410.5478
       1949  |   228.7341   141.8211     1.61   0.141    -92.08754    549.5558
       1950  |   269.7332   142.5671     1.89   0.091    -52.77601    592.2425
       1951  |   389.0968   173.2614     2.25   0.051    -2.847737    781.0414
       1952  |   407.3494   186.2776     2.19   0.057    -14.03991    828.7386
       1953  |   544.8882    229.695     2.37   0.042     25.28199    1064.494
       1954  |     556.86   208.9162     2.67   0.026     84.25866    1029.461
             |
       _cons |   557.2252   119.7887     4.65   0.001     286.2443    828.2061
-------------+----------------------------------------------------------------
     sigma_u |  964.10875
     sigma_e |  241.65446
         rho |  .94088802   (fraction of variance due to u_i)
------------------------------------------------------------------------------

Alas, my industry dummies are omitted as well. So just do away with the state dummies.